CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a Continuation of PCT International Application No. PCT/JP2013/005293 filed on Sep. 6, 2013, which claims priority under 35 U.S.C. §119(a) to Japanese Patent Application No. 2012-202352 filed on Sep. 14, 2012. Each of the above applications is hereby expressly incorporated by reference, in its entirety, into the present application. 
    
    
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to a zoom lens and an imaging apparatus. In particular, the present invention relates to a zoom lens used in an electronic camera, such as a digital camera, a camera for broadcasting, a camera for surveillance and a camera for film making, and also to an imaging apparatus including the zoom lens. 
     Description of the Related Art 
     In zoom lenses used in imaging apparatuses, such as a video camera and an electronic still camera using imaging devices, such as a CCD (Charge Coupled Device) and a CMOS (Complementary Metal Oxide Semiconductor), as recording media, a request for higher variable magnification ratios is increasing. As types of zoom lenses achieving high variable magnification ratios, a four-group-type zoom lens in which a positive group, a negative group, a positive group and a positive group are arranged in this order from the object side, or in which a positive group, a negative group, a positive group and a negative group are arranged in this order from the object side, or the like and a five-group-type zoom lens in which a positive group, a negative group, a positive group, a positive group and a positive group are arranged in this order from the object side, or in which a positive group, a negative group, a positive group, a negative group and a positive group are arranged in this order from the object side, or the like are known (for example, Japanese Unexamined Patent Publication No. 2011-186417 (Patent Document 1), Japanese Unexamined Patent Publication No. 2011-123337 (Patent Document 2), Japanese Unexamined Patent Publication No. 2009-294513 (Patent Document 3), and Japanese Unexamined Patent Publication No. 2009-251280 (Patent Document 4)). 
     SUMMARY OF THE INVENTION 
     Patent Document 1 discloses zoom lenses having variable magnification ratios of 28 in Examples 8 through 11. Patent Document 2 discloses zoom lenses having variable magnification ratios of 20 through 30. Patent Document 3 discloses zoom lenses having variable magnification ratios of 25 through 30. 
     One of major problems to be addressed in zoom lenses having high variable magnification ratios is balancing an optical performance, especially, chromatic aberrations at a telephoto side and the size of the lens system. 
     In the zoom lenses disclosed in Patent Document 1, aberrations are very excellently corrected. However, the extension amount of lens groups (the optical total length at a telephoto end) is rather large with respect to a focal length at a telephoto end. Therefore, when the variable magnification ratio is further increased while the zoom lens has the aforementioned configuration and arrangement of refractive power, the size of the zoom lens becomes extremely large. When the variable magnification ratio is increased, the size of a camera on which the lens is to be mounted should be increased so as to correspond to the increase in the variable magnification ratio. However, since the size of cameras demanded in markets is limited to some extent, it is not desirable that the size of the cameras simply increases in proportion to the increase in the variable magnification ratio. 
     Preventing the size of a lens system from becoming large even if a variable magnification ratio is increased is the same as reducing the size of the system without sacrificing its optical performance, such as chromatic aberrations at the telephoto side, in the example of Patent Document 1. For that purpose, there is room for improvement, for example, in selection of material used in the first lens group and the arrangement of refractive power in the first lens group. In four-group or five-group zoom lenses as described above, the first lens group generally consists of a cemented lens of a negative lens and a positive lens arranged closest to the object side, and one or two positive lenses. 
     In Patent Document 1, the first lens uses glass having an Abbe number of 25.4, and the second lens uses glass having an Abbe number of 64.2 or 70.2. For example, when the size of the system is tried to be reduced or a variable magnification ratio is tried to be increased while an increase in chromatic aberrations is suppressed in this configuration, the Abbe number of the material used in the second lens may be shifted further toward a low dispersion side, and correction may be performed by using anomalous dispersion properties. Generally, when a material having anomalous dispersion properties is used, the cost tends to increase. Therefore, although the cost must be taken into consideration, the material needs to be selected based on required specification and optical performance. After selection, the lens configuration and the arrangement of refractive power, especially, refractive power in the first lens group, the second lens group and the like need to be set in a most appropriate manner so that the size of the system does not become too large. 
     Further, when the Abbe number of a material used in a first lens that is a negative lens is set further toward a low dispersion side, that is advantageous to correction of a secondary spectrum. Patent Document 2 discloses an example in which a material having an Abbe number of 33.3 is used in the first lens. However, a variable magnification ratio remains at 29.9 times. Further, Patent Document 3 discloses an example in which anomalous dispersion glass having an Abbe number of 95.0 is used in the second lens. However, there is a problem that a production cost increases. A variable magnification ratio remains at 30 also in this example. 
     In Patent Document 4, variable magnification ratios of 39.6 times through 58.3 times are achieved by making the first lens group consist of four lenses. However, there is a problem that the size of the whole lens system becomes large. Further, the diameters of lenses arranged in the first lens group are overwhelmingly large, compared with those of lenses arranged in the other groups. Therefore, even if glass of expensive material is not used, a problem of increasing cost is big. 
     In view of the foregoing circumstances, it is an object of the present invention to provide a zoom lens in small size in which various aberrations are excellently corrected while the zoom lens has a high variable magnification ratio, and also an imaging apparatus including the zoom lens. 
     A zoom lens of the present invention consists of a first lens group having positive refractive power, a second lens group having negative refractive power, a third lens group having positive refractive power, a fourth lens group having negative refractive power, and a fifth lens group having positive refractive power in this order from an object side. Further, distances between the lens groups change during magnification change, and the first lens group is positioned closer to the object side in a telephoto end state than its position in a wide angle end state. Further, the first lens group consists of three lenses of an 11th lens having negative refractive power, a 12th lens having positive refractive power and a 13th lens having positive refractive power in this order from the object side. Further, the following conditional expressions are satisfied:
 
1.75&lt;Nd11  (1);
 
28&lt;νd11&lt;44  (2);
 
63&lt;νd12  (3); and
 
0.020&lt;| f 2|/ ft&lt; 0.050  (4), where
 
     Nd11: a refractive index of the 11-th lens for d-line, 
     νd11: an Abbe number of the 11-th lens for d-line, 
     νd12: an Abbe number of the 12-th lens for d-line, 
     f2: a focal length of the second lens group, and 
     ft: a focal length of an entire system at a telephoto end. 
     In the zoom lens of the present invention, it is desirable that the second lens group includes at least one positive lens, and that the following conditional expression is satisfied:
 
15&lt;νd2p&lt;23  (5), where
 
     νd2p: an Abbe number of the at least one positive lens in the second lens group for d-line. 
     Further, it is desirable that the following conditional expression is satisfied:
 
50&lt;νd13&lt;75  (6), where
 
     νd13: an Abbe number of the 13th lens. 
     It is desirable that the third lens group includes at least one cemented lens including a positive lens, and that the following conditional expression is satisfied:
 
65&lt;νd3pc  (7), where
 
     νd3pc: an Abbe number of the positive lens constituting the at least one cemented lens for d-line. 
     Here, when plural positive lenses included in a cemented lens or lenses in the third lens group are present, as in a case that a cemented lens consisting of three or more lenses is present or a case that plural cemented lenses are present, at least one of the positive lenses included in the cemented lens or lenses in the third lens group should satisfy conditional expression (7). 
     Further, it is desirable that the following conditional expression is satisfied:
 
8.5&lt; f 1/| f 2|&lt;16.0  (8), where
 
     f1: a focal length of the first lens group. 
     Further, it is desirable that the following conditional expression is satisfied:
 
0.3&lt;| f 4|/( fw×ft )1/2&lt;1.4  (9), where
 
     f4: a focal length of the fourth lens group, and 
     fw: a focal length of an entire system at a wide angle end. 
     Further, it is desirable that the following conditional expression is satisfied:
 
0.3&lt; f 5/| f 4|&lt;1.5  (10), where
 
     f5: a focal length of the fifth lens group, and 
     f4: a focal length of the fourth lens group. 
     Further, it is desirable that at least the first lens group, the second lens group, the third lens group and the fourth lens group move in such a manner that a distance between the first lens group and the second lens group increases, and a distance between the second lens group and the third lens group decreases, and a distance between the third lens group and the fourth lens group increases and a distance between the fourth lens group and the fifth lens group increases in the telephoto end state than their distances in the wide angle end state, respectively. 
     It is desirable that the second lens group consists of four lenses of a negative lens, a negative lens, and a cemented lens of a positive lens and a negative lens in this order from the object side. 
     Further, it is desirable that the third lens group includes at least two positive lenses and at least two negative lenses. 
     It is desirable that the fifth lens group consists of one lens. 
     Further, it is desirable that the fifth lens group is always fixed. 
     It is desirable that the fourth lens group consists of two lenses of a positive lens and a negative lens. 
     It is desirable that focusing is performed by moving the fourth lens group. 
     Further, it is desirable that the following conditional expressions are satisfied:
 
1.78&lt;Nd11  (1-1);
 
29&lt;νd11&lt;43  (2-1);
 
66&lt;νd12&lt;85  (3-1); and
 
0.023&lt;| f 2|/ ft&lt; 0.050  (4-1).
 
     Further, it is more desirable that the following conditional expressions are satisfied:
 
1.78&lt;Nd11  (1-1);
 
30&lt;νd11&lt;42  (2-2);
 
66&lt;νd12&lt;85  (3-1); and
 
0.027&lt;| f 2|/ ft&lt; 0.050  (4-2).
 
     Further, it is desirable that the second lens group includes at least one positive lens, and that the following conditional expression is satisfied:
 
16&lt;νd2p&lt;22  (5-1).
 
     Further, it is desirable that the following conditional expression is satisfied:
 
52&lt;νd13&lt;72  (6-1).
 
     Further, it is desirable that the third lens group includes at least one cemented lens including a positive lens, and that the following conditional expression is satisfied:
 
67&lt;νd3pc  (7-1).
 
     Further, it is more desirable that the following conditional expression is satisfied:
 
80&lt;νd3pc  (7-2).
 
     Further, it is desirable that the following conditional expression is satisfied:
 
9.0&lt; f 1/| f 2|&lt;15.0  (8-1).
 
     Further, it is more desirable that the following conditional expression is satisfied:
 
10.0&lt; f 1/| f 2|&lt;14.0  (8-2).
 
     Further, it is desirable that the following conditional expression is satisfied:
 
0.4&lt;| f 4|/( fw×ft )1/2&lt;1.3  (9-1).
 
     Further, it is more desirable that the following conditional expression is satisfied:
 
0.5&lt;| f 4|/( fw×ft )1/2&lt;1.1  (9-2).
 
     Further, it is desirable that the following conditional expression is satisfied:
 
0.4&lt; f 5/| f 4|&lt;1.3  (10-1).
 
     Further, it is more desirable that the following conditional expression is satisfied:
 
0.5&lt; f 5/| f 4|&lt;1.2  (10-2).
 
     An imaging apparatus of the present invention includes the aforementioned zoom lens of the present invention. 
     The zoom lens of the present invention consists of a first lens group having positive refractive power, a second lens group having negative refractive power, a third lens group having positive refractive power, a fourth lens group having negative refractive power, and a fifth lens group having positive refractive power in this order from an object side. Further, distances between the lens groups change during magnification change, and the first lens group is positioned closer to the object side in a telephoto end state than its position in a wide angle end state. Further, the first lens group consists of three lenses of an 11th lens having negative refractive power, a 12th lens having positive refractive power and a 13th lens having positive refractive power in this order from the object side. Further, the following conditional expressions are satisfied. Therefore, it is possible to provide a zoom lens in small size in which various aberrations are excellently corrected while the zoom lens has a high variable magnification ratio.
 
1.75&lt;Nd11  (1);
 
28&lt;νd11&lt;44  (2);
 
63&lt;νd12  (3); and
 
0.020&lt;| f 2|/ ft&lt; 0.050  (4).
 
     Further, the imaging apparatus of the present invention includes the zoom lens of the present invention. Therefore, it is possible to obtain high-image-quality video images at high variable magnification ratios, and to reduce the size of the apparatus. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a cross section illustrating the lens configuration of a zoom lens according to an embodiment of the present invention (also Example 1); 
         FIG. 2  is a cross section illustrating paths of movement of lens groups in the zoom lens; 
         FIG. 3  is a cross section illustrating the lens configuration of a zoom lens in Example 2 of the present invention; 
         FIG. 4  is a cross section illustrating the lens configuration of a zoom lens in Example 3 of the present invention; 
         FIG. 5  is a cross section illustrating the lens configuration of a zoom lens in Example 4 of the present invention; 
         FIG. 6  is a cross section illustrating the lens configuration of a zoom lens in Example 5 of the present invention; 
         FIG. 7  is a cross section illustrating the lens configuration of a zoom lens in Example 6 of the present invention; 
         FIG. 8  is a cross section illustrating the lens configuration of a zoom lens in Example 7 of the present invention; 
         FIG. 9  is aberration diagrams (Sections A through L) of the zoom lens in Example 1 of the present invention; 
         FIG. 10  is aberration diagrams (Sections A through L) of the zoom lens in Example 2 of the present invention; 
         FIG. 11  is aberration diagrams (Sections A through L) of the zoom lens in Example 3 of the present invention; 
         FIG. 12  is aberration diagrams (Sections A through L) of the zoom lens in Example 4 of the present invention; 
         FIG. 13  is aberration diagrams (Sections A through L) of the zoom lens in Example 5 of the present invention; 
         FIG. 14  is aberration diagrams (Sections A through L) of the zoom lens in Example 6 of the present invention; 
         FIG. 15  is aberration diagrams (Sections A through L) of the zoom lens in Example 7 of the present invention; and 
         FIG. 16  is a schematic diagram illustrating the configuration of an imaging apparatus according to an embodiment of the present invention. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Next, embodiments of the present invention will be described in detail with reference to drawings.  FIG. 1  is a cross section illustrating the lens configuration of a zoom lens according to an embodiment of the present invention.  FIG. 2  is a cross section illustrating paths of movement of lens groups in the zoom lens. The example of the configuration illustrated in  FIGS. 1 and 2  is also the configuration of a zoom lens in Example 1, which will be described later. In  FIGS. 1 and 2 , a left side is an object side, and a right side is an image side. 
     This zoom lens consists of first lens group G 1  having positive refractive power, second lens group G 2  having negative refractive power, aperture stop St, third lens group G 3  having positive refractive power, fourth lens group G 4  having negative refractive power, and fifth lens group G 5  having positive refractive power along optical axis Z in this order from an object side. Further, distances between the lens groups change during magnification change, and first lens group G 1  is positioned closer to the object side in a telephoto end state than its position in a wide angle end state. Here, aperture stop St illustrated in  FIGS. 1 and 2  does not necessarily represent the size nor the shape of the aperture stop, but the position of the aperture stop on optical axis Z. 
     When this zoom lens is applied to an imaging apparatus, it is desirable to arrange a cover glass, a prism, and various filters, such as an infrared-ray-cut filter and a low-pass filter, between an optical system and image plane Sim based on the configuration of a camera on which the lens is mounted. Therefore,  FIGS. 1 and 2  illustrate an example in which parallel-flat-plate-shaped optical members PP, which is assumed to be these elements, is arranged between fifth lens group G 5  and image plane Sim. 
     First lens group G 1  consists of three lenses of 11th lens L 11  having negative refractive power, 12th lens L 12  having positive refractive power and 13th lens L 13  having positive refractive power in this order from the object side. 
     For the purpose of obtaining a zoom lens having a high variable magnification ratio, and in which desirable optical performance, such as chromatic aberrations, and desirable size and cost are achieved in a well-balanced manner, it is necessary to set especially the material of a lens or lenses arranged in first lens group G 1 , the arrangement of refractive power in first lens group G 1  and the arrangement of refractive power in second lens group G 2  in a most appropriate manner. 
     Therefore, the zoom lens in an embodiment of the present invention is configured so that the following conditional expressions (1), (2), (3) and (4) are satisfied:
 
1.75&lt;Nd11  (1);
 
28&lt;νd11&lt;44  (2);
 
63&lt;νd12  (3); and
 
0.020&lt;| f 2|/ ft&lt; 0.050  (4), where
 
     Nd11: a refractive index of the 11-th lens for d-line, 
     νd11: an Abbe number of the 11-th lens for d-line, 
     νd12: an Abbe number of the 12-th lens for d-line, 
     f2: a focal length of the second lens group, and 
     ft: a focal length of an entire system at a telephoto end. 
     Conditional expression (1) defines the refractive index of 11th lens L 11 . If the value is lower than the lower limit of conditional expression (1), a Petzval sum of overcorrection is generated, and it becomes difficult to suppress curvature of field. 
     Conditional expression (2) defines the Abbe number of 11th lens L 11 . If the value is lower than the lower limit of conditional expression (2), when achromatization is performed by a combination of 11th lens L 11  and a positive lens or lenses arranged in first lens group G 1 , a difference in dispersion between 11th lens L 11  and the positive lens or lenses becomes large, and the refractive power of a lens or lenses in first lens group G 1  becomes weak. That is advantageous to correction of a spherical aberration, but it becomes difficult to suppress generation of chromatic aberrations on a short wavelength side at a telephoto side. In contrast, if the value exceeds the upper limit of conditional expression (2), the refractive power of each lens arranged in first lens group G 1  becomes strong. Therefore, it becomes difficult to correct especially a spherical aberration at a telephoto side. 
     Conditional expression (3) defines the Abbe number of 12th lens L 12 . If the value is lower than the lower limit of conditional expression (3), it becomes difficult to correct a longitudinal chromatic aberration at a telephoto side. Especially, when correction of chromatic aberrations by a combination of 11th lens L 11  made of material satisfying conditional expression (2) and 12th lens L 12  is considered, the refractive power of 12th lens L 12  becomes strong. Consequently, it becomes difficult to correct a spherical aberration and curvature of field at a telephoto side. 
     Conditional expression (4) defines a relationship between the focal length of second lens group G 2  and the focal length of an entire system at a telephoto end. When the value is lower than the lower limit of conditional expression (4), the refractive power of second lens group G 2  becomes too strong, and correction of various aberrations becomes difficult. It becomes difficult to correct especially curvature of field at a wide angle end. In contrast, if the value exceeds the upper limit of conditional expression (4), the refractive power of second lens group G 2  is insufficient, and does not contribute to the variable magnification ratio, or the size of the whole lens barrel becomes large as the total length of the zoom lens becomes long or the diameter of a lens or lenses constituting first lens group G 1  becomes large. 
     When the following conditional expressions (1-1), (2-1), (3-1) and (4-1) are satisfied, more excellent characteristics are achievable:
 
1.78&lt;Nd11  (1-1);
 
29&lt;νd11&lt;43  (2-1);
 
66&lt;νd12&lt;85  (3-1); and
 
0.023&lt;| f 2|/ ft&lt; 0.050  (4-1).
 
     If a material exceeding the upper limit of conditional expression (3-1) is used as the material of 12th lens L 12 , the anomalous dispersion properties become high. Therefore, that is advantageous to correction of chromatic aberrations. However, the production cost increases. Therefore, it is more desirable to select a material that does not exceed the upper limit of conditional expression (3-1), depending on required specification and optical performance. 
     When the following conditional expressions (1-1), (2-2), (3-1) and (4-2) are satisfied, more excellent characteristics are achievable:
 
1.78&lt;Nd11  (1-1);
 
30&lt;νd11&lt;42  (2-2);
 
66&lt;νd12&lt;85  (3-1); and
 
0.027&lt;| f 2|/ ft&lt; 0.050  (4-2).
 
     In a zoom lens according to an embodiment of the present invention, it is desirable that second lens group G 2  includes at least one positive lens, and that the following conditional expression (5) is satisfied. Conditional expression (5) defines the Abbe number of a positive lens or lenses arranged in second lens group G 2 . If the value is lower than the lower limit of conditional expression (5), it becomes difficult to suppress a secondary spectrum. In contrast, if the value exceeds the upper limit of conditional expression (5), it becomes impossible to effectively perform primary achromatization. When the following conditional expression (5-1) is satisfied, more excellent properties are achievable:
 
15&lt;νd2p&lt;23  (5); and
 
16&lt;νd2p&lt;22  (5-1), where
 
     νd2p: an Abbe number of the at least one positive lens in the second lens group for d-line. 
     Further, it is desirable that the following conditional expression (6) is satisfied. Conditional expression (6) defines the Abbe number of 13th lens L 13 . If the value is outside the range of conditional expression (6), it becomes difficult to correct a longitudinal chromatic aberration and a lateral chromatic aberration in a well-balanced manner through the entire zoom range. Especially, if the value is lower than the lower limit of conditional expression (6), it becomes difficult to correct a longitudinal chromatic aberration at a telephoto side. In contrast, if the value exceeds the upper limit of conditional expression (6), it becomes difficult to correct a lateral chromatic aberration at a wide angle side. When the following conditional expression (6-1) is satisfied, more excellent properties are achievable.
 
50&lt;νd13&lt;75  (6); and
 
52&lt;νd13&lt;72  (6-1), where
 
     νd13: an Abbe number of the 13th lens. 
     Further, it is desirable that third lens group G 3  includes at least one cemented lens including a positive lens, and that the following conditional expression (7) is satisfied. Conditional expression (7) defines the Abbe number of a positive lens constituting the cemented lens arranged in third lens group G 3 . For the purpose of reducing the size of the zoom lens or the like, when the negative refractive power of second lens group G 2  is increased in such a manner that the value is lower than the upper limit of conditional expression (4), or when a positive lens satisfying conditional expression (5) is arranged, these lenses are made of material of high refractive index and high dispersion. In that case, chromatic aberrations in second lens group G 2  tend to be undercorrected. If the value is lower than the lower limit of conditional expression (7), chromatic aberrations generated in second lens group G 2  are not fully corrected. When the following conditional expression (7-1) is satisfied, and more desirably, when the following conditional expression (7-2) is satisfied, more excellent properties are achievable:
 
65&lt;νd3pc  (7);
 
67&lt;νd3pc  (7-1); and
 
80&lt;νd3pc  (7-2), where
 
     νd3pc: an Abbe number of the positive lens constituting the at least one cemented lens for d-line. 
     Further, it is desirable that the following conditional expression (8) is satisfied. Conditional expression (8) defines a relationship between the focal length of first lens group G 1  and the focal length of second lens group G 2 . If the value is lower than the lower limit of conditional expression (8), the refractive power of first lens group G 1  becomes strong, and that is advantageous to reduction in size. However, aberrations generated in first lens group G 1  increase. Further, it becomes difficult to correct a lateral chromatic aberration generated at a wide angle side. Or, the refractive power of second lens group G 2  becomes weak, and does not contribute to the variable magnification ratio, or the total length of the zoom lens becomes long. In contrast, if the value exceeds the upper limit of conditional expression (8), the refractive power of first lens group G 1  becomes weak, and the total length of the lens becomes long, and the outer diameter of first lens group G 1  becomes large. Or, the refractive power of second lens group G 2  becomes strong, and aberrations generated in second lens group G 2  increase. When the following conditional expression (8-1) is satisfied, and more desirably, when the following conditional expression (8-2) is satisfied, more excellent properties are achievable:
 
8.5&lt; f 1/| f 2|&lt;16.0  (8);
 
9.0&lt; f 1/| f 2|&lt;15.0  (8-1); and
 
10.0&lt; f 1/| f 2|&lt;14.0  (8-2), where
 
     f1: a focal length of the first lens group. 
     It is desirable that the following conditional expression (9) is satisfied. Conditional expression (9) defines a relationship between the focal length of fourth lens group G 4  and the focal length of the entire system at a wide angle end and at a telephoto end. If the value is lower than the lower limit of conditional expression (9), the refractive power of fourth lens group G 4  becomes strong. Therefore, that is advantageous to reducing the size of the zoom lens. However, aberrations generated in fourth lens group G 4  increase. Therefore, it becomes difficult to excellently correct aberrations through the entire zoom range. In contrast, if the value exceeds the upper limit of conditional expression (9), the refractive power of fourth lens group G 4  becomes weak. Therefore, it becomes difficult to reduce the size of the zoom lens. When the following conditional expression (9-1) is satisfied, and more desirably, when the following conditional expression (9-2) is satisfied, more excellent properties are achievable:
 
0.3&lt;| f 4|/( fw×ft )1/2&lt;1.4  (9);
 
0.4&lt;| f 4|/( fw×ft )1/2&lt;1.3  (9-1); and
 
0.5&lt;| f 4|/( fw×ft )1/2&lt;1.1  (9-2), where
 
     f4: a focal length of the fourth lens group, and 
     fw: a focal length of an entire system at a wide angle end. 
     Further, it is desirable that following conditional expression (10) is satisfied. Conditional expression (10) defines the ratio of the focal length of fifth lens group G 5  to the focal length of fourth lens group G 4 . If the value is lower than the lower limit of conditional expression (10), the refractive power of fifth lens group G 5  becomes strong, and it becomes difficult to correct a coma aberration at a wide angle side. In contrast, if the value exceeds the upper limit of conditional expression (10), the refractive power of fourth lens group G 4  becomes strong, and it becomes difficult to correct a spherical aberration at a telephoto side. When the following conditional expression (10-1) is satisfied, and more desirably, when the following conditional expression (10-2) is satisfied, more excellent properties are achievable:
 
0.3&lt; f 5/| f 4|&lt;1.5  (10);
 
0.4&lt; f 5/| f 4|&lt;1.3  (10-1); and
 
0.5&lt; f 5/| f 4|&lt;1.2  (10-2), where
 
     f5: a focal length of the fifth lens group, and 
     f4: a focal length of the fourth lens group. 
     Further, it is desirable that at least first lens group G 1 , second lens group G 2 , third lens group G 3  and fourth lens group G 4  move in such a manner that a distance between first lens group G 1  and second lens group G 2  increases, and a distance between second lens group G 2  and third lens group G 3  decreases, and a distance between third lens group G 3  and fourth lens group G 4  increases and a distance between fourth lens group G 4  and fifth lens group G 5  increases in the telephoto end state than their distances in the wide angle end state, respectively. Accordingly, the variable magnification ratio is easily increased. 
     Further, it is desirable that second lens group G 2  consists of four lenses of a negative lens, a negative lens, and a cemented lens of a positive lens and a negative lens in this order from the object side. When two negative single lenses are arranged closer to the object side in second lens group G 2  in this manner, it is possible to make the position of an object-side principal point of second lens group G 2  closer to first lens group G 1 . Therefore, it is possible to reduce the size of first lens group G 1  for both of the diameter of first lens group G 1  and the size of first lens group G 1  in the direction of the optical axis. 
     Further, it is desirable that third lens group G 3  includes at least two positive lenses and at least two negative lenses. Accordingly, it is possible to correct aberrations in a well-balanced manner through the entire zoom range even if F-number FNo. is reduced. Further, that is advantageous also to correction of a longitudinal chromatic aberration. 
     Further, it is desirable that fifth lens group G 5  consists of one lens. Accordingly, it is possible to achieve reduction in size and cost. 
     Further, it is desirable that fifth lens group G 5  does not have a movement mechanism, and is always fixed. Accordingly, when the zoom lens is mounted on an imaging apparatus, such as a digital camera, it is possible to reduce adhesion of unwanted particles or dust to an imaging device. 
     Further, it is desirable that fourth lens group G 4  consists of two lenses of a positive lens and a negative lens. Accordingly, it is possible to suppress a fluctuation of aberrations caused by the movement of fourth lens group G 4  to a low level. 
     Further, it is desirable that focusing is performed by moving fourth lens group G 4 . When focusing is performed in this manner by using fourth lens group G 4 , which consists of a small number of lens or lenses, and the diameter of which is small, compared with the other lens groups, it is possible to increase the speed of focusing. 
     Specifically, in the zoom lens of the present invention, it is desirable to use glass, as a material arranged closest to the object side. Alternatively, transparent ceramic may be used. 
     When the zoom lens of the present invention is used in tough conditions, it is desirable that a multi-layer coating for protection is applied to the zoom lens. Further, an anti-reflection coating for reducing ghost light during use or the like may be applied to the zoom lens in addition to the coating for protection. 
       FIG. 1  illustrates an example in which optical member PP is arranged between the lens system and image plane Sim. Instead of arranging various filters, such as a low-pass filter and a filter that cuts a specific wavelength band, and the like between the lens system and image plane Sim, the various filters may be arranged between lenses. Alternatively, a coating having a similar action to the various filters may be applied to a lens surface of one of the lenses. 
     Next, numerical value examples of the zoom lens of the present invention will be described. 
     First, the zoom lens in Example 1 will be described.  FIG. 1  is a cross section illustrating the lens configuration of the zoom lens in Example 1. In  FIG. 1  and  FIGS. 3 through 8  corresponding to Examples 2 through 7, which will be described later, optical member PP is also illustrated, and the left side is an object side, and the right side is an image side. Illustrated aperture stop St does not necessarily represent the size nor the shape of the aperture stop, but the position of the aperture stop on optical axis Z. 
     The zoom lens in Example 1 consists of first lens group G 1  having positive refractive power, second lens group G 2  having negative refractive power, aperture stop St, third lens group G 3  having positive refractive power, fourth lens group G 4  having negative refractive power, and fifth lens group G 5  having positive refractive power in this order from an object side. 
     First lens group G 1  consists of three lenses of negative lens L 11 , positive lens L 12  cemented with negative lens L 11 , and positive lens L 13  in this order from the object side. The cemented lens consisting of negative lens L 11  and positive lens L 12  has an effect of correcting a longitudinal chromatic aberration at a telephoto side. Positive lens L 13  has an effect of correcting curvature of field at a telephoto end. Further, since first lens group G 1  consists of three lenses, reduction in the size and cost of the lens system is achieved. 
     Second lens group G 2  consists of four lenses of negative lens L 21 , negative lens L 22 , positive lens L 23  and negative lens L 24  cemented with positive lens L 23  in this order from the object side. When two negative single lenses are sequentially arranged from the object side, it is possible to make the position of an object-side principal point of second lens group G 2  closer to first lens group G 1 . Therefore, it is possible to reduce the diameter of first lens group G 1 . Further, the cemented lens consisting of positive lens L 23  and negative lens L 24  has an effect of correcting a lateral chromatic aberration at a wide angle end. 
     Third lens group G 3  consists of seven lenses of positive lens L 31 , negative lens L 32  cemented with positive lens L 31 , positive lens L 33 , negative lens L 34  cemented with positive lens L 33 , positive lens L 35  having an aspheric surface shape, negative lens L 36  and positive lens L 37  cemented with negative lens L 36  in this order from the object side. The cemented lens consisting of positive lens L 31  and negative lens L 32  has an effect of correcting a spherical aberration and a longitudinal chromatic aberration through an entire variable magnification range. The cemented lens consisting of positive lens L 33  and negative lens L 34  has an effect of correcting a longitudinal chromatic aberration and a lateral chromatic aberration through an entire variable magnification range. Positive lens L 35  having an aspheric surface shape has an effect of correcting a spherical aberration and curvature of field at a telephoto side. The cemented lens consisting of negative lens L 36  and positive lens L 37  has an effecting of correcting a lateral chromatic aberration through an entire variable magnification range. 
     Fourth lens group G 4  consists of two lenses of negative lens L 41  and positive lens L 42  having an aspheric surface shape in this order from the object side. When a positive lens and a negative lens are arranged, it is possible to suppress a fluctuation of chromatic aberrations caused by movement of fourth lens group G 4  to a low level. 
     Fifth lens group G 5  consists of one lens of positive lens L 51  having an aspheric surface shape. Positive lens L 51  has an effect of correcting distortion and curvature of field through an entire variable magnification range. Further, when fifth lens group G 5  consists of one lens, reduction in size, weight and cost is achieved. 
     In the zoom lens, first lens group G 1 , second lens group G 2 , third lens group G 3  and the fourth lens group G 4  move in such a manner that a distance between first lens group G 1  and second lens group G 2  increases, and a distance between second lens group G 2  and third lens group G 3  decreases, and a distance between third lens group G 3  and fourth lens group G 4  increases and a distance between fourth lens group G 4  and fifth lens group G 5  increases in the telephoto end state than their distances in the wide angle end state, respectively. Further, fifth lens group G 5  is fixed. 
     Focusing is performed by moving fourth lens group G 4 . 
     The zoom lens is configured in such a manner that the cemented lens consisting of negative lens L 36  and positive lens L 37  is movable in a direction perpendicular to the optical axis to prevent image shaking. When the lens for preventing image shaking consists of a cemented lens, it is possible to suppress a fluctuation of chromatic aberrations caused by movement of the lens to a low level. 
     Table 1 shows basic lens data of the zoom lens in Example 1. Table 2 shows data about the specification of the zoom lens in Example 1. Table 3 shows data about moving surface distances. Table 4 shows data about aspheric surface coefficients. In the following descriptions, the meanings of signs in the tables will be described by using the tables of Example 1, as an example. The meanings of signs in the tables of Examples 2 through 7 are basically similar to those of Example 1. 
     In the lens data of Table 1, a column of Si shows the surface number of an i-th surface (i=1, 2, 3 . . . ) when a surface of composition elements closest to the object side is the first surface and the surface numbers sequentially increase toward the image side. A column of Ri shows the curvature radius of the i-th surface. A column of Di shows a distance, on optical axis Z, between the i-th surface and (i+1)th surface. Further, a column of Ndj shows the refractive index of a j-th optical element (j=1, 2, 3 . . . ) for d-line (wavelength is 587.6 nm) when an optical element closest to the object side is the first optical element and j sequentially increases toward the image side. A column of νdj similarly shows the Abbe number of the j-th optical element for d-line (wavelength is 587.6 nm). 
     Here, the sign of a curvature radius is positive when a surface shape is convex toward the object side, and negative when a surface shape is convex toward the image side. The basic lens data show data including aperture stop St and optical member PP. In the column of surface numbers, the term “(STOP)” is written together with the surface number of a surface corresponding to aperture stop St. 
     Further, in the lens data of Table 1, “DD[i]” is written in a row of a surface distance that changes during magnification change. Further, a value at the bottom of the column of Di is a distance between an image-side surface of optical member PP and image plane Sim. 
     Data about specification in Table 2 show values of a zoom ratio, focal length f′, F-number FNo. and full angle of view 2ω for each of wide angle, middle and telephoto. 
     In the basic lens data, data about specification and data about moving surface distances, degree is used as the unit of an angle, and mm is used as the unit of a length. However, since an optical system is usable by proportionally enlarging the optical system or by proportionally reducing the optical system, other appropriate units may be used. 
     In the lens data of Table 1, mark “*” is attached to the surface numbers of aspheric surfaces. Further, a numerical value of a paraxial curvature radius is used as the curvature radius of an aspheric surface. The data about aspheric surface coefficients in Table 4 show surface numbers Si of aspheric surfaces and aspheric surface coefficients about the aspheric surfaces. The aspheric surface coefficients are values of coefficients KA, Am (m=3, 4, 5, . . . 20) in an aspheric surface equation represented by the following equation (A):
 
 Zd=C·h   2 /{1+(1· KA·C   2   ·h   2 ) 1/2   }+ΣAm·h   m   (A),
 
where,
 
     Zd: the depth of an aspheric surface (the length of a perpendicular from a point on the aspheric surface at height h to a flat plane that contacts with the vertex of the aspheric surface and is perpendicular to the optical axis), 
     h: height (a length from the optical axis), 
     C: a reciprocal of a paraxial curvature radius, and 
     KA, Am: aspheric surface coefficients (m=3, 4, 5, . . . 20). 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 EXAMPLE 1 - LENS DATA 
               
             
          
           
               
                   
                   
                   
                 Ndj 
                 vdj 
               
               
                 Si 
                 Ri 
                 Di 
                 (REFRAC- 
                 (ABBE 
               
               
                 (SURFACE 
                 (CURVATURE 
                 (SURFACE 
                 TIVE 
                 NUM- 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 BER) 
               
               
                   
               
             
          
           
               
                  1 
                 190.5660 
                 1.51 
                 1.83400 
                 37.16 
               
               
                  2 
                 47.6350 
                 5.95 
                 1.48749 
                 70.23 
               
               
                  3 
                 −255.1477 
                 0.11 
                   
                   
               
               
                  4 
                 48.4503 
                 4.78 
                 1.60311 
                 60.64 
               
               
                  5 
                 661.0686 
                 DD[5] 
                   
                   
               
               
                  6 
                 102.1754 
                 0.86 
                 1.83481 
                 42.73 
               
               
                  7 
                 8.5281 
                 4.46 
                   
                   
               
               
                  8 
                 −17.7998 
                 0.88 
                 1.90366 
                 31.32 
               
               
                  9 
                 76.2591 
                 0.11 
                   
                   
               
               
                 10 
                 24.0501 
                 3.35 
                 1.94595 
                 17.98 
               
               
                 11 
                 −37.8880 
                 0.80 
                 1.72916 
                 54.68 
               
               
                 12 
                 117.0060 
                 DD[12] 
                   
                   
               
               
                 13(STOP) 
                 ∞ 
                 1.50 
                   
                   
               
               
                 14 
                 9.1387 
                 4.91 
                 1.49700 
                 81.54 
               
               
                 15 
                 −15.6820 
                 0.88 
                 1.80400 
                 46.58 
               
               
                 16 
                 −24.3585 
                 0.20 
                   
                   
               
               
                 17 
                 −157.6928 
                 2.09 
                 1.80100 
                 34.97 
               
               
                 18 
                 −20.2930 
                 0.88 
                 1.76200 
                 40.10 
               
               
                 19 
                 15.3575 
                 0.41 
                   
                   
               
               
                 *20  
                 7.6717 
                 2.40 
                 1.56864 
                 58.62 
               
               
                 *21  
                 9.5799 
                 3.60 
                   
                   
               
               
                 22 
                 14.3576 
                 0.76 
                 1.61772 
                 49.81 
               
               
                 23 
                 8.1030 
                 3.10 
                 1.49700 
                 81.54 
               
               
                 24 
                 −80.1409 
                 DD[24] 
                   
                   
               
               
                 25 
                 19.7873 
                 0.80 
                 1.79952 
                 42.22 
               
               
                 26 
                 7.1947 
                 0.51 
                   
                   
               
               
                 *27  
                 8.3796 
                 2.10 
                 1.53391 
                 55.89 
               
               
                 *28  
                 10.9061 
                 DD[28] 
                   
                   
               
               
                 *29  
                 469.3592 
                 2.60 
                 1.53391 
                 55.89 
               
               
                 *30  
                 −7.3909 
                 1.10 
                   
                   
               
               
                 31 
                 ∞ 
                 0.80 
                 1.51680 
                 64.20 
               
               
                 32 
                 ∞ 
                 2.55 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 EXAMPLE 1 - SPECIFICATION (d-LINE) 
               
             
          
           
               
                   
                 WIDE ANGLE 
                 MIDDLE 
                 TELEPHOTO 
               
               
                   
               
             
          
           
               
                 ZOOM MAGNIFICATION 
                 1.0 
                 7.7 
                 47.1 
               
               
                 RATIO 
                   
                   
                   
               
               
                 f′ 
                 4.44 
                 34.30 
                 209.39 
               
               
                 FNo. 
                 2.98 
                 6.04 
                 6.80 
               
               
                 2ω[°] 
                 92.2 
                 12.4 
                 2.0 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 EXAMPLE 1 - ZOOM DISTANCE 
               
             
          
           
               
                   
                 WIDE ANGLE 
                 MIDDLE 
                 TELEPHOTO 
               
               
                   
               
             
          
           
               
                   
                 DD[5] 
                 0.58 
                 48.12 
                 73.66 
               
               
                   
                 DD[12] 
                 37.99 
                 13.41 
                 2.45 
               
               
                   
                 DD[24] 
                 2.65 
                 8.91 
                 14.05 
               
               
                   
                 DD[28] 
                 2.91 
                 14.27 
                 18.46 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                 EXAMPLE 1 - ASPHERIC SURFACE COEFFICIENT 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 SURFACE NUMBER 
               
             
          
           
               
                   
                 20 
                 21 
                 27 
               
               
                   
               
               
                 KA 
                 1.0000000E+00 
                 1.0000000E+00 
                 1.0000000E+00 
               
               
                 A3 
                 2.6840949E−05 
                 9.6307265E−06 
                 −4.5533282E−04 
               
               
                 A4 
                 −4.0306307E−04 
                 7.3621072E−05 
                 −1.2918285E−03 
               
               
                 A5 
                 2.5198056E−06 
                 −2.6145919E−06 
                 3.2078380E−04 
               
               
                 A6 
                 −9.5112872E−06 
                 −4.5823516E−06 
                 −1.0687848E−04 
               
               
                 A7 
                 −2.6237590E−06 
                 −3.5876523E−06 
                 −1.6051072E−05 
               
               
                 A8 
                 2.1471331E−07 
                 −4.5619492E−07 
                 1.6277933E−05 
               
               
                 A9 
                 −7.1179356E−09 
                 2.6697425E−08 
                 1.0136115E−06 
               
               
                 A10 
                 −1.6215254E−09 
                 3.7583410E−08 
                 −1.2342175E−06 
               
               
                 A11 
                 −3.2592544E−09 
                 5.5519309E−09 
                 1.8817130E−09 
               
               
                 A12 
                 −5.5670711E−10 
                 −1.4229821E−09 
                 −2.8331680E−08 
               
               
                 A13 
                 −2.1318200E−11 
                 −9.5993415E−10 
                 −3.1637844E−09 
               
               
                 A14 
                 6.1660347E−11 
                 1.2919125E−10 
                 3.3690565E−09 
               
               
                 A15 
                 9.4765495E−12 
                 3.2299721E−12 
                 1.1375237E−09 
               
               
                 A16 
                 2.2768029E−13 
                 7.2930789E−13 
                 2.0965110E−10 
               
               
                 A17 
                 −4.2298985E−13 
                 1.4521435E−13 
                 −1.9468436E−11 
               
               
                 A18 
                 −1.9822796E−13 
                 2.5577813E−14 
                 −5.7315055E−11 
               
               
                 A19 
                 −1.9192457E−14 
                 −4.5492169E−16 
                 1.1707052E−11 
               
               
                 A20 
                 1.0838208E−14 
                 −1.5156669E−15 
                 −8.8917300E−13 
               
               
                   
               
             
          
           
               
                   
                 SURFACE NUMBER 
               
             
          
           
               
                   
                 28 
                 29 
                 30 
               
               
                   
               
               
                 KA 
                 1.0000000E+00 
                 1.0000000E+00 
                 1.0000000E+00 
               
               
                 A3 
                 −7.8046373E−04 
                 4.1389256E−03 
                 6.4276109E−03 
               
               
                 A4 
                 −9.0593396E−04 
                 −1.7407938E−03 
                 −2.1835610E−03 
               
               
                 A5 
                 −3.6516432E−04 
                 −1.8614071E−04 
                 3.7348826E−04 
               
               
                 A6 
                 9.5544087E−05 
                 5.8185227E−05 
                 −3.8126997E−05 
               
               
                 A7 
                 3.5954706E−05 
                 −7.1731920E−07 
                 −6.2222952E−06 
               
               
                 A8 
                 −1.3611027E−05 
                 −1.0090005E−06 
                 1.3099766E−06 
               
               
                 A9 
                 −2.4072648E−06 
                 −4.8213431E−08 
                 3.4186661E−07 
               
               
                 A10 
                 1.8850003E−07 
                 6.7023680E−08 
                 7.0027606E−09 
               
               
                 A11 
                 6.3401887E−07 
                 4.3549929E−09 
                 −5.2174530E−09 
               
               
                 A12 
                 −9.3299572E−08 
                 4.5644935E−10 
                 −1.3116009E−09 
               
               
                 A13 
                 −3.9007838E−09 
                 −1.5366353E−10 
                 −6.1769255E−11 
               
               
                 A14 
                 −4.4058901E−09 
                 −7.7327336E−11 
                 2.4659817E−11 
               
               
                 A15 
                 −6.7430841E−10 
                 −1.3480473E−11 
                 1.9511726E−12 
               
               
                 A16 
                 4.6896009E−11 
                 −2.8760743E−13 
                 −1.3535040E−12 
               
               
                 A17 
                 −5.3144357E−12 
                 3.0669242E−13 
                 −3.9170140E−14 
               
               
                 A18 
                 7.7085581E−11 
                 1.2921973E−13 
                 1.9739940E−14 
               
               
                 A19 
                 −2.4348533E−12 
                 1.5038695E−14 
                 1.8928268E−14 
               
               
                 A20 
                 −2.8770423E−12 
                 −4.6753424E−15 
                 −2.5889239E−15 
               
               
                   
               
             
          
         
       
     
       FIG. 9 , Sections A through L are aberration diagrams of the zoom lens in Example 1.  FIG. 9 , Sections A through D illustrate a spherical aberration, astigmatism, distortion and a lateral chromatic aberration at wide angle, respectively.  FIG. 9 , Sections E through H illustrate a spherical aberration, astigmatism, distortion and a lateral chromatic aberration at middle, respectively.  FIG. 9 , Sections I through L illustrate a spherical aberration, astigmatism, distortion and a lateral chromatic aberration at telephoto, respectively. 
     Aberration diagrams of a spherical aberration, astigmatism and distortion show aberrations when d-line (wavelength is 587.6 nm) is a reference wavelength. In the aberration diagram of the spherical aberration, aberrations for d-line (wavelength is 587.6 nm), C-line (wavelength is 656.3 nm), F-line (wavelength is 486.1 nm) and g-line (wavelength is 435.8 nm) are indicated by a solid line, a long broken line, a short broken line and a gray solid line, respectively. In the aberration diagram of the astigmatism, an aberration in a sagittal direction and an aberration in a tangential direction are indicated by a solid line and a broken line, respectively. In the aberration diagram of the lateral chromatic aberration, an aberration for C-line (wavelength is 656.3 nm), an aberration for F-line (wavelength is 486.1 nm) and an aberration for g-line (wavelength is 435.8 nm) are indicated by a long broken line, a short broken line and a gray solid line, respectively. In the aberration diagram of the spherical aberration, Fno. represents an F-number. In the other aberration diagrams, ω means a half angle of view. 
     Next, a zoom lens in Example 2 will be described.  FIG. 3  is a cross section illustrating the lens configuration of the zoom lens in Example 2. 
     In the zoom lens of Example 2, only the configuration of third lens group G 3  differs from the zoom lens of Example 1. 
     In the zoom lens of Example 2, third lens group G 3  consists of five lenses of positive lens L 31 , negative lens L 32  cemented with positive lens L 31 , positive lens L 33 , negative lens L 34  cemented with positive lens L 33 , and positive lens L 35  having an aspheric surface shape in this order from the object side. The cemented lens consisting of positive lens L 31  and negative lens L 32  has an effect of correcting a spherical aberration and a longitudinal chromatic aberration through an entire variable magnification range. The cemented consisting of positive lens L 33  and negative lens L 34  has an effect of correcting a longitudinal chromatic aberration and a lateral chromatic aberration through an entire variable magnification range. Positive lens L 35  having an aspheric surface shape has an effect of correcting a spherical aberration and curvature of field at a telephoto side. 
     The zoom lens may be configured in such a manner that the whole third lens group G 3  is movable in a direction perpendicular to the optical axis to prevent image shaking. 
     Table 5 shows basic lens data of the zoom lens in Example 2. Table 6 shows data about the specification of the zoom lens in Example 2. Table 7 shows data about moving surface distances. Table 8 shows data about aspheric surface coefficients.  FIG. 10 , Sections A through L illustrate aberration diagrams. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 EXAMPLE 2 - LENS DATA 
               
             
          
           
               
                   
                   
                   
                 Ndj 
                 vdj 
               
               
                 Si 
                 Ri 
                 Di 
                 (REFRAC- 
                 (ABBE 
               
               
                 (SURFACE 
                 (CURVATURE 
                 (SURFACE 
                 TIVE 
                 NUM- 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 BER) 
               
               
                   
               
             
          
           
               
                  1 
                 126.0626 
                 1.51 
                 1.90366 
                 31.32 
               
               
                  2 
                 64.3848 
                 5.63 
                 1.49700 
                 81.54 
               
               
                  3 
                 −320.7357 
                 0.10 
                   
                   
               
               
                  4 
                 56.2313 
                 4.80 
                 1.59282 
                 68.63 
               
               
                  5 
                 200.0000 
                 DD[5] 
                   
                   
               
               
                  6 
                 130.1741 
                 0.95 
                 1.83481 
                 42.71 
               
               
                  7 
                 8.0771 
                 4.80 
                   
                   
               
               
                  8 
                 −20.7044 
                 0.88 
                 1.80610 
                 40.92 
               
               
                  9 
                 54.3462 
                 0.10 
                   
                   
               
               
                 10 
                 19.2493 
                 3.41 
                 1.92285 
                 20.88 
               
               
                 11 
                 −32.9858 
                 0.88 
                 1.88300 
                 40.76 
               
               
                 12 
                 57.2176 
                 DD[12] 
                   
                   
               
               
                 13(STOP) 
                 ∞ 
                 1.50 
                   
                   
               
               
                 14 
                 8.7978 
                 4.81 
                 1.49700 
                 81.54 
               
               
                 15 
                 −11.4527 
                 0.88 
                 1.82232 
                 41.92 
               
               
                 16 
                 −23.4480 
                 0.20 
                   
                   
               
               
                 17 
                 44.1961 
                 4.00 
                 1.71299 
                 53.87 
               
               
                 18 
                 −11.3799 
                 0.88 
                 1.79952 
                 42.22 
               
               
                 19 
                 47.6322 
                 0.40 
                   
                   
               
               
                 *20  
                 7.0327 
                 2.50 
                 1.56854 
                 58.62 
               
               
                 *21  
                 7.3629 
                 DD[21] 
                   
                   
               
               
                 22 
                 89.3762 
                 0.80 
                 1.83400 
                 37.16 
               
               
                 23 
                 7.8423 
                 0.60 
                   
                   
               
               
                 *24  
                 8.5045 
                 2.20 
                 1.53391 
                 55.89 
               
               
                 *25  
                 32.8653 
                 DD[25] 
                   
                   
               
               
                 *26  
                 3459.9189 
                 2.70 
                 1.53391 
                 55.89 
               
               
                 *27  
                 −7.3838 
                 1.10 
                   
                   
               
               
                 28 
                 ∞ 
                 0.80 
                 1.51680 
                 64.20 
               
               
                 29 
                 ∞ 
                 2.75 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 EXAMPLE 2 - SPECIFICATION (d-LINE) 
               
             
          
           
               
                   
                 WIDE ANGLE 
                 MIDDLE 
                 TELEPHOTO 
               
               
                   
               
             
          
           
               
                 ZOOM MAGNIFICATION 
                 1.0 
                 7.5 
                 47.1 
               
               
                 RATIO 
                   
                   
                   
               
               
                 f′ 
                 4.26 
                 31.93 
                 200.44 
               
               
                 FNo. 
                 3.18 
                 5.21 
                 6.76 
               
               
                 2ω[°] 
                 95.8 
                 13.4 
                 2.4 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 EXAMPLE 2 - ZOOM DISTANCE 
               
             
          
           
               
                   
                 WIDE ANGLE 
                 MIDDLE 
                 TELEPHOTO 
               
               
                   
               
             
          
           
               
                   
                 DD[5] 
                 0.58 
                 47.49 
                 76.42 
               
               
                   
                 DD[12] 
                 29.83 
                 10.33 
                 1.80 
               
               
                   
                 DD[21] 
                 2.87 
                 7.58 
                 11.44 
               
               
                   
                 DD[25] 
                 2.00 
                 14.27 
                 19.26 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                 EXAMPLE 2 - ASPHERIC SURFACE COEFFICIENT 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 SURFACE NUMBER 
               
             
          
           
               
                   
                 20 
                 21 
                 24 
               
               
                   
               
               
                 KA 
                 0.0000000E+00 
                 0.0000000E+00 
                 9.9858849E−01 
               
               
                 A3 
                 3.5194825E−05 
                 2.4877428E−05 
                 −7.9448771E−04 
               
               
                 A4 
                 −9.1259035E−05 
                 2.7370653E−04 
                 −1.4106330E−04 
               
               
                 A5 
                 −3.4848057E−05 
                 9.7021289E−06 
                 −1.8868792E−04 
               
               
                 A6 
                 −2.8299394E−06 
                 −1.7770410E−05 
                 5.3762494E−06 
               
               
                 A7 
                 −1.6336898E−06 
                 −4.6460453E−06 
                 2.2735299E−05 
               
               
                 A8 
                 −3.6190710E−07 
                 −5.2997309E−07 
                 4.1530284E−06 
               
               
                 A9 
                 −1.0333655E−07 
                 −7.6318024E−08 
                 1.1800520E−09 
               
               
                 A10 
                 −1.2786129E−08 
                 −3.4229251E−09 
                 −4.0983097E−07 
               
               
                 A11 
                 −1.8566621E−09 
                 5.0110763E−10 
                 −6.2334264E−08 
               
               
                 A12 
                 1.8000150E−10 
                 2.3836828E−10 
                 −2.8331680E−08 
               
               
                 A13 
                 1.0931229E−10 
                 4.4141144E−11 
                 −3.1637844E−09 
               
               
                 A14 
                 2.5380661E−11 
                 7.0902347E−12 
                 3.3690565E−09 
               
               
                 A15 
                 9.4765495E−12 
                 3.2299721E−12 
                 1.1375237E−09 
               
               
                 A16 
                 2.2768029E−13 
                 7.2930789E−13 
                 2.0965110E−10 
               
               
                 A17 
                 −4.2298985E−13 
                 1.4521435E−13 
                 −1.9468436E−11 
               
               
                 A18 
                 −1.9822796E−13 
                 2.5577813E−14 
                 −5.7315055E−11 
               
               
                 A19 
                 −1.9192457E−14 
                 −4.5492169E−16 
                 1.1707052E−11 
               
               
                 A20 
                 1.0838208E−14 
                 −1.5156669E−15 
                 −8.8917300E−13 
               
               
                   
               
             
          
           
               
                   
                 SURFACE NUMBER 
               
             
          
           
               
                   
                 25 
                 26 
                 27 
               
               
                   
               
               
                 KA 
                 −3.4356281E−02 
                 −1.5919206E−02 
                 6.0897382E−01 
               
               
                 A3 
                 −3.7929976E−04 
                 3.8177383E−03 
                 5.3885518E−03 
               
               
                 A4 
                 −6.9961451E−04 
                 −1.6572658E−03 
                 −1.7916006E−03 
               
               
                 A5 
                 1.0168216E−04 
                 5.3459736E−05 
                 5.5287290E−04 
               
               
                 A6 
                 7.3843981E−06 
                 7.2602184E−05 
                 −4.3329082E−05 
               
               
                 A7 
                 −1.6226768E−06 
                 −4.8974929E−06 
                 −9.9407611E−06 
               
               
                 A8 
                 2.0881076E−07 
                 −1.8692134E−06 
                 1.1038055E−06 
               
               
                 A9 
                 3.1749046E−07 
                 1.5162102E−08 
                 3.1755849E−07 
               
               
                 A10 
                 2.7569861E−07 
                 5.9534773E−08 
                 3.0676327E−08 
               
               
                 A11 
                 2.8387925E−08 
                 9.1638701E−09 
                 −2.3009594E−09 
               
               
                 A12 
                 6.0966231E−09 
                 5.7322777E−10 
                 −1.1315956E−09 
               
               
                 A13 
                 −3.9007838E−09 
                 −2.0838522E−10 
                 −1.8971726E−10 
               
               
                 A14 
                 −4.4058901E−09 
                 −7.7327336E−11 
                 −1.2784100E−11 
               
               
                 A15 
                 −6.7430841E−10 
                 −1.3480473E−11 
                 1.9511726E−12 
               
               
                 A16 
                 4.6896009E−11 
                 −2.8760743E−13 
                 −5.4179089E−14 
               
               
                 A17 
                 −5.3144357E−12 
                 3.0669242E−13 
                 −3.9170140E−14 
               
               
                 A18 
                 7.7085581E−11 
                 1.2921973E−13 
                 1.9739940E−14 
               
               
                 A19 
                 −2.4348533E−12 
                 1.5038695E−14 
                 1.8928268E−14 
               
               
                 A20 
                 −2.8770423E−12 
                 −4.6753424E−15 
                 −2.5889239E−15 
               
               
                   
               
             
          
         
       
     
     Next, a zoom lens in Example 3 will be described.  FIG. 4  is a cross section illustrating the lens configuration of the zoom lens in Example 3. 
     The shape of the zoom lens in Example 3 is similar to that of the zoom lens in Example 2. 
     Table 9 shows basic lens data of the zoom lens in Example 3. Table 10 shows data about the specification of the zoom lens in Example 3. Table 11 shows data about moving surface distances. Table 12 shows data about aspheric surface coefficients.  FIG. 11 , Sections A through L illustrate aberration diagrams. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 9 
               
             
             
               
                   
               
               
                 EXAMPLE 3 - LENS DATA 
               
             
          
           
               
                   
                   
                   
                 Ndj 
                 vdj 
               
               
                 Si 
                 Ri 
                 Di 
                 (REFRAC- 
                 (ABBE 
               
               
                 (SURFACE 
                 (CURVATURE 
                 (SURFACE 
                 TIVE 
                 NUM- 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 BER) 
               
               
                   
               
             
          
           
               
                  1 
                 223.5393 
                 1.51 
                 1.80440 
                 39.60 
               
               
                  2 
                 53.9454 
                 6.68 
                 1.49700 
                 81.54 
               
               
                  3 
                 −186.7839 
                 0.10 
                   
                   
               
               
                  4 
                 50.2252 
                 4.80 
                 1.59282 
                 68.63 
               
               
                  5 
                 289.1225 
                 DD[5] 
                   
                   
               
               
                  6 
                 132.0095 
                 0.95 
                 1.83481 
                 42.71 
               
               
                  7 
                 8.2291 
                 4.80 
                   
                   
               
               
                  8 
                 −19.1341 
                 0.88 
                 1.80610 
                 40.92 
               
               
                  9 
                 56.2574 
                 0.10 
                   
                   
               
               
                 10 
                 20.8053 
                 3.46 
                 1.92286 
                 18.90 
               
               
                 11 
                 −51.1072 
                 0.88 
                 1.88300 
                 40.76 
               
               
                 12 
                 90.3183 
                 DD[12] 
                   
                   
               
               
                 13(STOP) 
                 ∞ 
                 1.50 
                   
                   
               
               
                 14 
                 8.6339 
                 4.81 
                 1.48749 
                 70.23 
               
               
                 15 
                 −11.3782 
                 0.88 
                 1.83400 
                 37.16 
               
               
                 16 
                 −23.7354 
                 0.20 
                   
                   
               
               
                 17 
                 47.7867 
                 4.27 
                 1.71299 
                 53.87 
               
               
                 18 
                 −11.0001 
                 0.88 
                 1.79952 
                 42.22 
               
               
                 19 
                 50.2516 
                 0.40 
                   
                   
               
               
                 *20  
                 7.0001 
                 2.50 
                 1.56864 
                 58.62 
               
               
                 *21  
                 7.3558 
                 DD[21] 
                   
                   
               
               
                 22 
                 74.9762 
                 0.80 
                 1.83400 
                 37.16 
               
               
                 23 
                 7.7289 
                 0.60 
                   
                   
               
               
                 *24  
                 8.3679 
                 2.20 
                 1.53391 
                 55.89 
               
               
                 *25  
                 30.5001 
                 DD[25] 
                   
                   
               
               
                 *26  
                 1086.5832 
                 2.70 
                 1.53391 
                 55.89 
               
               
                 *27  
                 −7.4023 
                 1.10 
                   
                   
               
               
                 28 
                 ∞ 
                 0.80 
                 1.51680 
                 64.20 
               
               
                 29 
                 ∞ 
                 2.75 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 10 
               
             
             
               
                   
               
               
                 EXAMPLE 3 - SPECIFICATION (d-LINE) 
               
             
          
           
               
                   
                 WIDE ANGLE 
                 MIDDLE 
                 TELEPHOTO 
               
               
                   
               
             
          
           
               
                 ZOOM MAGNIFICATION 
                 1.0 
                 7.5 
                 47.1 
               
               
                 RATIO 
                   
                   
                   
               
               
                 f′ 
                 4.35 
                 32.65 
                 204.95 
               
               
                 FNo. 
                 3.39 
                 5.41 
                 6.76 
               
               
                 2ω[°] 
                 94.8 
                 13.2 
                 2.4 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 11 
               
             
             
               
                   
               
               
                 EXAMPLE 3 - ZOOM DISTANCE 
               
             
          
           
               
                   
                 WIDE ANGLE 
                 MIDDLE 
                 TELEPHOTO 
               
               
                   
               
             
          
           
               
                   
                 DD[5] 
                 0.58 
                 47.35 
                 74.95 
               
               
                   
                 DD[12] 
                 31.45 
                 11.33 
                 1.81 
               
               
                   
                 DD[21] 
                 2.62 
                 7.36 
                 11.36 
               
               
                   
                 DD[25] 
                 3.28 
                 15.54 
                 18.67 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
           
               
                 TABLE 12 
               
               
                   
               
               
                 EXAMPLE 3 - ASPHERIC SURFACE COEFFICIENT 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 SURFACE NUMBER 
               
             
          
           
               
                   
                 20 
                 21 
                 24 
               
               
                   
               
               
                 KA 
                 0.0000000E+00 
                 0.0000000E+00 
                 9.9858849E−01 
               
               
                 A3 
                 3.5194825E−05 
                 2.4877428E−05 
                 −7.9448771E−04 
               
               
                 A4 
                 −9.1259035E−05 
                 2.7370653E−04 
                 −1.4106330E−04 
               
               
                 A5 
                 −3.4848057E−05 
                 9.7021289E−06 
                 −1.8868792E−04 
               
               
                 A6 
                 −2.8299394E−06 
                 −1.7770410E−05 
                 5.3762494E−06 
               
               
                 A7 
                 −1.6336898E−06 
                 −4.6460453E−06 
                 2.2735299E−05 
               
               
                 A8 
                 −3.6190710E−07 
                 −5.2997309E−07 
                 4.1530284E−06 
               
               
                 A9 
                 −1.0333655E−07 
                 −7.6318024E−08 
                 1.1800520E−09 
               
               
                 A10 
                 −1.2786129E−08 
                 −3.4229251E−09 
                 −4.0983097E−07 
               
               
                 A11 
                 −1.8566621E−09 
                 5.0110763E−10 
                 −8.2334264E−08 
               
               
                 A12 
                 1.8000150E−10 
                 2.3836828E−10 
                 −2.8331680E−08 
               
               
                 A13 
                 1.0931229E−10 
                 4.4141144E−11 
                 −3.1637844E−09 
               
               
                 A14 
                 2.5380661E−11 
                 7.0902347E−12 
                 3.3690565E−09 
               
               
                 A15 
                 9.4765495E−12 
                 3.2299721E−12 
                 1.1375237E−09 
               
               
                 A16 
                 2.2768029E−13 
                 7.2930789E−13 
                 2.0965110E−10 
               
               
                 A17 
                 −4.2298985E−13 
                 1.4521435E−13 
                 −1.9468436E−11 
               
               
                 A18 
                 −1.9822796E−13 
                 2.5577813E−14 
                 −5.7315055E−11 
               
               
                 A19 
                 −1.9192457E−14 
                 −4.5492169E−16 
                 1.1707052E−11 
               
               
                 A20 
                 1.0838208E−14 
                 −1.5156669E−15 
                 −8.8917300E−13 
               
               
                   
               
             
          
           
               
                   
                 SURFACE NUMBER 
               
             
          
           
               
                   
                 25 
                 26 
                 27 
               
               
                   
               
               
                 KA 
                 −3.4356281E−02 
                 −1.5919206E−02 
                 6.0897382E−01 
               
               
                 A3 
                 −3.7929976E−04 
                 3.8177383E−03 
                 5.3885518E−03 
               
               
                 A4 
                 −6.9961451E−04 
                 −1.6572658E−03 
                 −1.7916006E−03 
               
               
                 A5 
                 1.0168216E−04 
                 5.3459736E−05 
                 5.5287290E−04 
               
               
                 A6 
                 7.3843981E−06 
                 7.2602184E−05 
                 −4.3329082E−05 
               
               
                 A7 
                 −1.6226768E−06 
                 −4.8974929E−06 
                 −9.9407611E−06 
               
               
                 A8 
                 2.0881076E−07 
                 −1.8692134E−06 
                 1.1038055E−06 
               
               
                 A9 
                 3.1749046E−07 
                 1.5162102E−08 
                 3.1755849E−07 
               
               
                 A10 
                 2.7569861E−07 
                 5.9534773E−08 
                 3.0676327E−08 
               
               
                 A11 
                 2.8387925E−08 
                 9.1638701E−09 
                 −2.3009594E−09 
               
               
                 A12 
                 6.0966231E−09 
                 5.7322777E−10 
                 −1.1315956E−09 
               
               
                 A13 
                 −3.9007838E−09 
                 −2.0838522E−10 
                 −1.8971726E−10 
               
               
                 A14 
                 −4.4058901E−09 
                 −7.7327336E−11 
                 −1.2784100E−11 
               
               
                 A15 
                 −6.7430841E−10 
                 −1.3480473E−11 
                 1.9511726E−12 
               
               
                 A16 
                 4.6896009E−11 
                 −2.8760743E−13 
                 −5.4179089E−14 
               
               
                 A17 
                 −5.3144357E−12 
                 3.0669242E−13 
                 −3.9170140E−14 
               
               
                 A18 
                 7.7085581E−11 
                 1.2921973E−13 
                 1.9739940E−14 
               
               
                 A19 
                 −2.4348533E−12 
                 1.5038695E−14 
                 1.8928268E−14 
               
               
                 A20 
                 −2.8770423E−12 
                 −4.6753424E−15 
                 −2.5889239E−15 
               
               
                   
               
             
          
         
       
     
     Next, a zoom lens in Example 4 will be described.  FIG. 5  is a cross section illustrating the lens configuration of the zoom lens in Example 4. 
     The shape of the zoom lens in Example 4 is also similar to that of the zoom lens in Example 2. 
     Table 13 shows basic lens data of the zoom lens in Example 4. Table 14 shows data about the specification of the zoom lens in Example 4. Table 15 shows data about moving surface distances. Table 16 shows data about aspheric surface coefficients.  FIG. 12 , Sections A through L illustrate aberration diagrams. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 13 
               
             
             
               
                   
               
               
                 EXAMPLE 4 - LENS DATA 
               
             
          
           
               
                   
                   
                   
                 Ndj 
                 vdj 
               
               
                 Si 
                 Ri 
                 Di 
                 (REFRAC- 
                 (ABBE 
               
               
                 (SURFACE 
                 (CURVATURE 
                 (SURFACE 
                 TIVE 
                 NUM- 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 BER) 
               
               
                   
               
             
          
           
               
                  1 
                 249.0543 
                 1.51 
                 1.91082 
                 35.25 
               
               
                  2 
                 59.7272 
                 5.08 
                 1.49700 
                 81.54 
               
               
                  3 
                 −157.8441 
                 0.10 
                   
                   
               
               
                  4 
                 52.2327 
                 4.60 
                 1.71299 
                 53.87 
               
               
                  5 
                 21.49513 
                 DD[5] 
                   
                   
               
               
                  6 
                 91.5449 
                 0.95 
                 1.83481 
                 42.71 
               
               
                  7 
                 8.1932 
                 4.80 
                   
                   
               
               
                  8 
                 −18.9326 
                 0.88 
                 1.80610 
                 40.92 
               
               
                  9 
                 59.7288 
                 0.10 
                   
                   
               
               
                 10 
                 20.2111 
                 3.41 
                 1.94595 
                 17.98 
               
               
                 11 
                 −52.4594 
                 0.89 
                 1.88300 
                 40.76 
               
               
                 12 
                 46.7052 
                 DD[12] 
                   
                   
               
               
                 13(STOP) 
                 ∞ 
                 1.50 
                   
                   
               
               
                 14 
                 8.7009 
                 4.81 
                 1.49700 
                 81.54 
               
               
                 15 
                 −11.3086 
                 0.88 
                 1.83481 
                 42.71 
               
               
                 16 
                 −22.1811 
                 0.20 
                   
                   
               
               
                 17 
                 48.6840 
                 3.61 
                 1.71299 
                 53.87 
               
               
                 18 
                 −11.6906 
                 0.88 
                 1.79952 
                 42.22 
               
               
                 19 
                 40.6208 
                 0.40 
                   
                   
               
               
                 *20  
                 7.1108 
                 2.50 
                 1.56864 
                 58.62 
               
               
                 *21  
                 7.5871 
                 DD[21] 
                   
                   
               
               
                 22 
                 92.3966 
                 0.80 
                 1.83400 
                 37.16 
               
               
                 23 
                 7.8599 
                 0.60 
                   
                   
               
               
                 *24  
                 9.0267 
                 2.20 
                 1.53391 
                 55.89 
               
               
                 *25  
                 31.9656 
                 DD[25] 
                   
                   
               
               
                 *26  
                 825.7211 
                 2.70 
                 1.53391 
                 55.89 
               
               
                 *27  
                 −7.1501 
                 1.10 
                   
                   
               
               
                 28 
                 ∞ 
                 0.80 
                 1.51680 
                 54.20 
               
               
                 29 
                 ∞ 
                 3.04 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 14 
               
             
             
               
                   
               
               
                 EXAMPLE 4 - SPECIFICATION (d-LINE) 
               
             
          
           
               
                   
                 WIDE ANGLE 
                 MIDDLE 
                 TELEPHOTO 
               
               
                   
               
             
          
           
               
                 ZOOM MAGNIFICATION 
                 1.0 
                 7.5 
                 56.0 
               
               
                 RATIO 
                   
                   
                   
               
               
                 f′ 
                 4.01 
                 30.07 
                 224.54 
               
               
                 FNo. 
                 3.22 
                 5.23 
                 6.84 
               
               
                 2ω[°] 
                 98.2 
                 14.0 
                 1.8 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 15 
               
             
             
               
                   
               
               
                 EXAMPLE 4 - ZOOM DISTANCE 
               
             
          
           
               
                   
                 WIDE ANGLE 
                 MIDDLE 
                 TELEPHOTO 
               
               
                   
               
             
          
           
               
                   
                 DD[5] 
                 0.58 
                 48.01 
                 77.60 
               
               
                   
                 DD[12] 
                 31.59 
                 11.98 
                 1.81 
               
               
                   
                 DD[21] 
                 3.07 
                 7.66 
                 12.93 
               
               
                   
                 DD[25] 
                 2.00 
                 14.55 
                 17.85 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
           
               
                 TABLE 16 
               
               
                   
               
               
                 EXAMPLE 4 - ASPHERIC SURFACE COEFFICIENT 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 SURFACE NUMBER 
               
             
          
           
               
                   
                 20 
                 21 
                 24 
               
               
                   
               
               
                 KA 
                 0.0000000E+00 
                 0.0000000E+00 
                 9.9858849E−01 
               
               
                 A3 
                 3.5194825E−05 
                 2.4877428E−05 
                 −7.9448771E−04 
               
               
                 A4 
                 −9.1259035E−05 
                 2.7370653E−04 
                 −1.4106330E−04 
               
               
                 A5 
                 −3.4848057E−05 
                 9.7021289E−06 
                 −1.8868792E−04 
               
               
                 A6 
                 −2.8299394E−06 
                 −1.7770410E−05 
                 5.3762494E−06 
               
               
                 A7 
                 −1.6336898E−06 
                 −4.6460453E−06 
                 2.2735299E−05 
               
               
                 A8 
                 −3.6190710E−07 
                 −5.2997309E−07 
                 4.1530284E−06 
               
               
                 A9 
                 −1.0333655E−07 
                 −7.6318024E−08 
                 1.1800520E−09 
               
               
                 A10 
                 −1.2786129E−08 
                 −3.4229251E−09 
                 −4.0983097E−07 
               
               
                 A11 
                 −1.8566621E−09 
                 5.0110763E−10 
                 −8.2334264E−08 
               
               
                 A12 
                 1.8000150E−10 
                 2.3836828E−10 
                 −2.8331680E−08 
               
               
                 A13 
                 −1.0931229E−10 
                 4.4141144E−11 
                 −3.1637844E−09 
               
               
                 A14 
                 2.5380661E−11 
                 7.0902347E−12 
                 3.3690565E−09 
               
               
                 A15 
                 9.4765495E−12 
                 3.2299721E−12 
                 1.1375237E−09 
               
               
                 A16 
                 2.2768029E−13 
                 7.2930789E−13 
                 2.0965110E−10 
               
               
                 A17 
                 −4.2298985E−13 
                 1.4521435E−13 
                 −1.9468436E−11 
               
               
                 A18 
                 −1.9822796E−13 
                 2.5577813E−14 
                 −5.7315055E−11 
               
               
                 A19 
                 −1.9192457E−14 
                 −4.5492169E−16 
                 1.1707052E−11 
               
               
                 A20 
                 1.0838208E−14 
                 −1.5156669E−15 
                 −8.8917300E−13 
               
               
                   
               
             
          
           
               
                   
                 SURFACE NUMBER 
               
             
          
           
               
                   
                 25 
                 26 
                 27 
               
               
                   
               
               
                 KA 
                 −3.4356281E−02 
                 −1.5919206E−02 
                 6.0897382E−01 
               
               
                 A3 
                 −3.7929976E−04 
                 3.8177383E−03 
                 5.3885518E−03 
               
               
                 A4 
                 −6.9961451E−04 
                 −1.6572658E−03 
                 −1.7916006E−03 
               
               
                 A5 
                 1.0168216E−04 
                 5.3459736E−05 
                 5.5287290E−04 
               
               
                 A6 
                 7.3843981E−06 
                 7.2602184E−05 
                 −4.3329062E−05 
               
               
                 A7 
                 −1.6226768E−06 
                 −4.8974929E−06 
                 −9.9407611E−06 
               
               
                 A8 
                 2.0881076E−07 
                 −1.8692134E−06 
                 1.1038055E−06 
               
               
                 A9 
                 3.1749046E−07 
                 1.5162102E−08 
                 3.1755849E−07 
               
               
                 A10 
                 2.7569861E−07 
                 5.9534773E−08 
                 3.0676327E−08 
               
               
                 A11 
                 2.8387925E−08 
                 9.1638701E−09 
                 −2.3009594E−09 
               
               
                 A12 
                 6.0966231E−09 
                 5.7322777E−10 
                 −1.1315956E−09 
               
               
                 A13 
                 −3.9007838E−09 
                 −2.0838522E−10 
                 −1.8971726E−10 
               
               
                 A14 
                 −4.4058901E−09 
                 −7.7327336E−11 
                 −1.2784100E−11 
               
               
                 A15 
                 −6.7430841E−10 
                 −1.3480473E−11 
                 1.9511726E−12 
               
               
                 A16 
                 4.6896009E−11 
                 −2.8760743E−13 
                 −5.4179089E−14 
               
               
                 A17 
                 −5.3144357E−12 
                 3.0669242E−13 
                 −3.9170140E−14 
               
               
                 A18 
                 7.7085581E−11 
                 1.2921973E−13 
                 1.9739940E−14 
               
               
                 A19 
                 −2.4348533E−12 
                 1.5038695E−14 
                 1.8928268E−14 
               
               
                 A20 
                 −2.8770423E−12 
                 −4.6753424E−15 
                 −2.5889239E−15 
               
               
                   
               
             
          
         
       
     
     Next, a zoom lens in Example 5 will be described.  FIG. 6  is a cross section illustrating the lens configuration of the zoom lens in Example 5. 
     The shape of the zoom lens in Example 5 is also similar to that of the zoom lens in Example 2. 
     Table 17 shows basic lens data of the zoom lens in Example 5. Table 18 shows data about the specification of the zoom lens in Example 5. Table 19 shows data about moving surface distances. Table 20 shows data about aspheric surface coefficients.  FIG. 13 , Sections A through L illustrate aberration diagrams. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 17 
               
             
             
               
                   
               
               
                 EXAMPLE 5 - LENS DATA 
               
             
          
           
               
                   
                 Ri 
                   
                 Ndj 
                   
               
               
                 Si 
                 (CURVA- 
                 Di 
                 (REFRAC- 
                 vdj 
               
               
                 (SURFACE 
                 TURE 
                 (SURFACE 
                 TIVE 
                 (ABBE 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 NUMBER) 
               
               
                   
               
             
          
           
               
                  1 
                 160.2199 
                 1.51 
                 1.91082 
                 35.25 
               
               
                  2 
                 61.1364 
                 5.37 
                 1.49700 
                 81.54 
               
               
                  3 
                 −205.8867 
                 0.10 
                   
                   
               
               
                  4 
                 51.9196 
                 4.63 
                 1.61800 
                 53.33 
               
               
                  5 
                 200.3257 
                 DD[5] 
                   
                   
               
               
                  6 
                 107.0743 
                 0.95 
                 1.83481 
                 42.71 
               
               
                  7 
                 8.0242 
                 4.80 
                   
                   
               
               
                  8 
                 −18.2149 
                 0.88 
                 1.90610 
                 40.92 
               
               
                  9 
                 71.9095 
                 0.10 
                   
                   
               
               
                 10 
                 20.0014 
                 3.41 
                 1.94595 
                 17.98 
               
               
                 11 
                 −69.0618 
                 0.88 
                 1.88300 
                 40.76 
               
               
                 12 
                 46.7003 
                 DD[12] 
                   
                   
               
               
                 13(STOP) 
                 ∞ 
                 1.50 
                   
                   
               
               
                 14 
                 8.7582 
                 4.81 
                 1.49700 
                 81.54 
               
               
                 15 
                 −11.5278 
                 0.88 
                 1.83481 
                 42.71 
               
               
                 16 
                 −21.9949 
                 0.20 
                   
                   
               
               
                 17 
                 50.2452 
                 3.54 
                 1.71299 
                 53.87 
               
               
                 18 
                 −11.9076 
                 0.88 
                 1.79952 
                 42.22 
               
               
                 19 
                 38.6290 
                 0.40 
                   
                   
               
               
                 *20  
                 7.1234 
                 2.50 
                 1.56864 
                 58.62 
               
               
                 *21  
                 7.7253 
                 DD[21] 
                   
                   
               
               
                 22 
                 80.5396 
                 0.80 
                 1.83400 
                 37.16 
               
               
                 23 
                 7.8803 
                 0.60 
                   
                   
               
               
                 *24  
                 9.1368 
                 2.20 
                 1.53391 
                 55.89 
               
               
                 *25  
                 32.4118 
                 DD[25] 
                   
                   
               
               
                 *26  
                 553.2121 
                 2.70 
                 1.53391 
                 55.89 
               
               
                 *27  
                 −7.1331 
                 1.10 
                   
                   
               
               
                 28 
                 ∞ 
                 0.80 
                 1.51680 
                 64.20 
               
               
                 29 
                 ∞ 
                 2.91 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 18 
               
             
             
               
                   
               
               
                 EXAMPLE 5 - SPECIFICATION (d-LINE) 
               
             
          
           
               
                   
                 WIDE ANGLE 
                 MIDDLE 
                 TELEPHOTO 
               
               
                   
               
             
          
           
               
                 ZOOM MAGNIFICATION 
                 1.0 
                 7.5 
                 58.8 
               
               
                 RATIO 
                   
                   
                   
               
               
                 f′ 
                 4.12 
                 30.91 
                 242.33 
               
               
                 FNo. 
                 3.30 
                 5.43 
                 6.78 
               
               
                 2ω[°] 
                 95.2 
                 13.6 
                 1.8 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 19 
               
             
             
               
                   
               
               
                 EXAMPLE 5 - ZOOM DISTANCE 
               
             
          
           
               
                   
                   
                 WIDE ANGLE 
                 MIDDLE 
                 TELEPHOTO 
               
               
                   
               
             
          
           
               
                   
                 DD[5] 
                 0.58 
                 47.70 
                 77.70 
               
               
                   
                 DD[12] 
                 30.39 
                 11.82 
                 1.80 
               
               
                   
                 DD[21] 
                 3.56 
                 8.63 
                 13.50 
               
               
                   
                 DD[25] 
                 2.14 
                 14.50 
                 16.95 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
           
               
                 TABLE 20 
               
               
                   
               
               
                 EXAMPLE 5 - ASPHERIC SURFACE COEFFICIENT 
               
               
                   
               
             
             
               
                 SURFACE NUMBER 
               
             
          
           
               
                   
                 20 
                 21 
                 24 
               
               
                   
               
               
                 KA 
                 0.0000000E+00 
                 0.0000000E+00 
                 9.9858849E−01 
               
               
                 A3 
                 3.5194825E−05 
                 2.4877428E−05 
                 −7.9448771E−04 
               
               
                 A4 
                 −9.1259035E−05 
                 2.7370653E−04 
                 −1.4106330E−04 
               
               
                 A5 
                 −3.4848057E−05 
                 9.7021289E−06 
                 −1.8868792E−04 
               
               
                 A6 
                 −2.8299394E−06 
                 −1.7770410E−05 
                 5.3762494E−06 
               
               
                 A7 
                 −1.6336898E−06 
                 −4.6460453E−06 
                 2.2735299E−05 
               
               
                 A8 
                 −3.6190710E−07 
                 −5.2997309E−07 
                 4.1530284E−06 
               
               
                 A9 
                 −1.0333655E−07 
                 −7.6318024E−08 
                 1.1800520E−09 
               
               
                 A10 
                 −1.2786129E−08 
                 −3.4229251E−09 
                 −4.0983097E−07 
               
               
                 A11 
                 −1.8566621E−09 
                 5.0110763E−10 
                 −8.2334264E−08 
               
               
                 A12 
                 1.8000150E−10 
                 2.3836828E−10 
                 −2.8331680E−08 
               
               
                 A13 
                 1.0931229E−10 
                 4.4141144E−11 
                 −3.1637844E−09 
               
               
                 A14 
                 2.5380661E−11 
                 7.0902347E−12 
                 3.3690565E−09 
               
               
                 A15 
                 9.4765495E−12 
                 3.2299721E−12 
                 1.1375237E−09 
               
               
                 A16 
                 2.2768029E−13 
                 7.2930789E−13 
                 2.0965110E−10 
               
               
                 A17 
                 −4.2298985E−13 
                 1.4521435E−13 
                 −1.9468436E−11 
               
               
                 A18 
                 −1.9822796E−13 
                 2.5577813E−14 
                 −5.7315055E−11 
               
               
                 A19 
                 −1.9192457E−14 
                 −4.5492169E−16 
                 1.1707052E−11 
               
               
                 A20 
                 1.0838208E−14 
                 −1.5156669E−15 
                 −8.8917300E−13 
               
               
                   
               
             
          
           
               
                   
                 SURFACE NUMBER 
               
             
          
           
               
                   
                 25 
                 26 
                 27 
               
               
                   
               
               
                 KA 
                 −3.4356281E−02 
                 −1.5919206E−02 
                 6.0897382E−01 
               
               
                 A3 
                 −3.7929976E−04 
                 3.8177383E−03 
                 5.3885518E−03 
               
               
                 A4 
                 −6.9961451E−04 
                 −1.6572658E−03 
                 −1.7916006E−03 
               
               
                 A5 
                 1.0168216E−04 
                 5.3459736E−05 
                 5.5287290E−04 
               
               
                 A6 
                 7.3843981E−06 
                 7.2602184E−05 
                 −4.3329082E−05 
               
               
                 A7 
                 −1.6226768E−06 
                 −4.8974929E−06 
                 −9.9407611E−06 
               
               
                 A8 
                 2.0881076E−07 
                 −1.8692134E−06 
                 1.1038055E−06 
               
               
                 A9 
                 3.1749046E−07 
                 1.5162102E−08 
                 3.1755849E−07 
               
               
                 A10 
                 2.7569861E−07 
                 5.9534773E−08 
                 3.0676327E−08 
               
               
                 A11 
                 2.8387925E−08 
                 9.1638701E−09 
                 −2.3009594E−09 
               
               
                 A12 
                 6.0966231E−09 
                 5.7322777E−10 
                 1.1315956E−09 
               
               
                 A13 
                 −3.9007838E−09 
                 −2.0838522E−10 
                 −1.8971726E−10 
               
               
                 A14 
                 −4.4058901E−09 
                 −7.7327336E−11 
                 −1.2784100E−11 
               
               
                 A15 
                 −6.7430841E−10 
                 −1.3480473E−11 
                 1.9511726E−12 
               
               
                 A16 
                 4.6896009E−11 
                 −2.8760743E−13 
                 −5.4179089E−14 
               
               
                 A17 
                 −5.3144357E−12 
                 3.0669242E−13 
                 −3.9170140E−14 
               
               
                 A18 
                 7.7085581E−11 
                 1.2921973E−13 
                 1.9739940E−14 
               
               
                 A19 
                 −2.4348533E−12 
                 1.5038695E−14 
                 1.8928268E−14 
               
               
                 A20 
                 −2.8770423E−12 
                 −4.6753424E−15 
                 −2.5889239E−15 
               
               
                   
               
             
          
         
       
     
     Next, a zoom lens in Example 6 will be described.  FIG. 7  is a cross section illustrating the lens configuration of the zoom lens in Example 6. 
     The shape of the zoom lens in Example 6 is also similar to that of the zoom lens in Example 2. 
     Table 21 shows basic lens data of the zoom lens in Example 6. Table 22 shows data about the specification of the zoom lens in Example 6. Table 23 shows data about moving surface distances. Table 24 shows data about aspheric surface coefficients.  FIG. 14 , Sections A through L illustrate aberration diagrams. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 21 
               
             
             
               
                   
               
               
                 EXAMPLE 6 - LENS DATA 
               
             
          
           
               
                   
                 Ri 
                   
                 Ndj 
                   
               
               
                 Si 
                 (CURVA- 
                 Di 
                 (REFRAC- 
                 vdj 
               
               
                 (SURFACE 
                 TURE 
                 (SURFACE 
                 TIVE 
                 (ABBE 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 NUMBER) 
               
               
                   
               
             
          
           
               
                  1 
                 246.6697 
                 1.51 
                 1.83400 
                 37.16 
               
               
                  2 
                 47.9587 
                 5.80 
                 1.59282 
                 68.63 
               
               
                  3 
                 −266.8129 
                 0.10 
                   
                   
               
               
                  4 
                 47.1889 
                 4.34 
                 1.62041 
                 60.29 
               
               
                  5 
                 206.4799 
                 DD[5] 
                   
                   
               
               
                  6 
                 58.0093 
                 0.95 
                 1.88300 
                 40.76 
               
               
                  7 
                 7.8001 
                 4.80 
                   
                   
               
               
                  8 
                 −19.6543 
                 0.88 
                 1.80400 
                 46.57 
               
               
                  9 
                 134.8211 
                 0.10 
                   
                   
               
               
                 10 
                 17.9126 
                 4.51 
                 1.92286 
                 20.88 
               
               
                 11 
                 −50.6965 
                 0.88 
                 1.88300 
                 40.76 
               
               
                 12 
                 35.1919 
                 DD[12] 
                   
                   
               
               
                 13(STOP) 
                 ∞ 
                 1.50 
                   
                   
               
               
                 14 
                 8.4999 
                 4.81 
                 1.49700 
                 81.54 
               
               
                 15 
                 −14.5662 
                 0.88 
                 1.83481 
                 42.71 
               
               
                 16 
                 −58.2230 
                 0.20 
                   
                   
               
               
                 17 
                 24.7619 
                 4.13 
                 1.62041 
                 60.29 
               
               
                 18 
                 −11.1393 
                 0.88 
                 1.79952 
                 42.22 
               
               
                 19 
                 −125.6267 
                 0.40 
                   
                   
               
               
                 *20  
                 7.6333 
                 2.50 
                 1.56864 
                 58.62 
               
               
                 *21  
                 8.5109 
                 DD[21] 
                   
                   
               
               
                 22 
                 −238.8755 
                 0.80 
                 1.83400 
                 37.16 
               
               
                 23 
                 7.6538 
                 0.60 
                   
                   
               
               
                 *24  
                 8.4290 
                 2.20 
                 1.53391 
                 55.89 
               
               
                 *25  
                 22.6778 
                 DD[25] 
                   
                   
               
               
                 *26  
                 −214748.3648 
                 2.70 
                 1.53391 
                 55.89 
               
               
                 *27  
                 −7.3590 
                 1.10 
                   
                   
               
               
                 28 
                 ∞ 
                 0.80 
                 1.51680 
                 64.20 
               
               
                 29 
                 ∞ 
                 2.75 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 22 
               
             
             
               
                   
               
               
                 EXAMPLE 6 - SPECIFICATION (d-LINE) 
               
             
          
           
               
                   
                 WIDE ANGLE 
                 MIDDLE 
                 TELEPHOTO 
               
               
                   
               
             
          
           
               
                 ZOOM MAGNIFICATION 
                 1.0 
                 6.3 
                 36.0 
               
               
                 RATIO 
                   
                   
                   
               
               
                 f′ 
                 4.45 
                 28.04 
                 160.30 
               
               
                 FNo. 
                 3.27 
                 4.95 
                 6.74 
               
               
                 2ω[°] 
                 91.2 
                 15.2 
                 3.0 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 23 
               
             
             
               
                   
               
               
                 EXAMPLE 6 - ZOOM DISTANCE 
               
             
          
           
               
                   
                 WIDE ANGLE 
                 MIDDLE 
                 TELEPHOTO 
               
               
                   
               
             
          
           
               
                   
                 DD[5] 
                 0.58 
                 42.42 
                 68.88 
               
               
                   
                 DD[12] 
                 28.16 
                 10.13 
                 1.87 
               
               
                   
                 DD[21] 
                 2.61 
                 6.18 
                 9.52 
               
               
                   
                 DD[25] 
                 2.00 
                 11.71 
                 17.66 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
           
               
                 TABLE 24 
               
               
                   
               
               
                 EXAMPLE 6 - ASPHERIC SURFACE COEFFICIENT 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 SURFACE NUMBER 
               
             
          
           
               
                   
                 20 
                 21 
                 24 
               
               
                   
               
               
                 KA 
                 0.0000000E+00 
                 0.0000000E+00 
                 9.9858849E−01 
               
               
                 A3 
                 3.5194825E−05 
                 2.4877428E−05 
                 −7.9448771E−04 
               
               
                 A4 
                 −9.1259035E−05 
                 2.7370653E−04 
                 −1.4106330E−04 
               
               
                 A5 
                 −3.4848057E−05 
                 9.7021289E−06 
                 −1.8868792E−04 
               
               
                 A6 
                 −2.8299394E−06 
                 −1.7770410E−05 
                 5.3762494E−06 
               
               
                 A7 
                 −1.6336898E−06 
                 −4.6460453E−06 
                 2.2735299E−05 
               
               
                 A8 
                 −3.6190710E−07 
                 −5.2997309E−07 
                 4.1530284E−06 
               
               
                 A9 
                 −1.0333655E−07 
                 −7.6318024E−08 
                 1.1800520E−09 
               
               
                 A10 
                 −1.2786129E−08 
                 −3.4229251E−09 
                 −4.0983097E−07 
               
               
                 A11 
                 −1.8566621E−09 
                 5.0110763E−10 
                 −8.2334264E−08 
               
               
                 A12 
                 1.8000150E−10 
                 2.3836828E−10 
                 −2.8331680E−08 
               
               
                 A13 
                 1.0931229E−10 
                 4.4141144E−11 
                 −3.1637844E−09 
               
               
                 A14 
                 2.5380661E−11 
                 7.0902347E−12 
                 3.3690565E−09 
               
               
                 A15 
                 9.4765495E−12 
                 3.2299721E−12 
                 1.1375237E−09 
               
               
                 A16 
                 2.2768029E−13 
                 7.2930789E−13 
                 2.0965110E−10 
               
               
                 A17 
                 −4.2298985E−13 
                 1.4521435E−13 
                 −1.9468436E−11 
               
               
                 A18 
                 −1.9822796E−13 
                 2.5577813E−14 
                 −5.7315055E−11 
               
               
                 A19 
                 −1.9192457E−14 
                 −4.5492169E−16 
                 1.1707052E−11 
               
               
                 A20 
                 1.0838208E−14 
                 −1.5156669E−15 
                 −8.8917300E−13 
               
               
                   
               
             
          
           
               
                   
                 SURFACE NUMBER 
               
             
          
           
               
                   
                 25 
                 26 
                 27 
               
               
                   
               
               
                 KA 
                 −3.4356281E−02 
                 −1.5919206E−02 
                 6.0897382E−01 
               
               
                 A3 
                 −3.7929976E−04 
                 3.8177383E−03 
                 5.3885518E−03 
               
               
                 A4 
                 −6.9961451E−04 
                 −1.6572658E−03 
                 −1.7916006E−03 
               
               
                 A5 
                 1.0168216E−04 
                 5.3459736E−05 
                 5.5287290E−04 
               
               
                 A6 
                 7.3843981E−06 
                 7.2602184E−05 
                 −4.3329082E−05 
               
               
                 A7 
                 −1.6226768E−06 
                 −4.8974929E−06 
                 −9.9407611E−06 
               
               
                 A8 
                 2.0881076E−07 
                 −1.8692134E−06 
                 1.1038055E−06 
               
               
                 A9 
                 3.1749046E−07 
                 1.5162102E−08 
                 3.1755849E−07 
               
               
                 A10 
                 2.7569861E−07 
                 5.9534773E−08 
                 3.0676327E−08 
               
               
                 A11 
                 2.8387925E−08 
                 9.1638701E−09 
                 −2.3009594E−09 
               
               
                 A12 
                 6.0966231E−09 
                 5.7322777E−10 
                 −1.1315956E−09 
               
               
                 A13 
                 −3.9007838E−09 
                 −2.0838522E−10 
                 −1.8971726E−10 
               
               
                 A14 
                 −4.4058901E−09 
                 −7.7327336E−11 
                 −1.2784100E−11 
               
               
                 A15 
                 −6.7430841E−10 
                 −1.3480473E−11 
                 1.9511726E−12 
               
               
                 A16 
                 4.6896009E−11 
                 −2.8760743E−13 
                 −5.4179089E−14 
               
               
                 A17 
                 −5.3144357E−12 
                 3.0669242E−13 
                 −3.9170140E−14 
               
               
                 A18 
                 7.7085581E−11 
                 1.2921973E−13 
                 1.9739940E−14 
               
               
                 A19 
                 −2.4348533E−12 
                 1.5038695E−14 
                 1.8928268E−14 
               
               
                 A20 
                 −2.8770423E−12 
                 −4.6753424E−15 
                 −2.5889239E−15 
               
               
                   
               
             
          
         
       
     
     Next, a zoom lens in Example 7 will be described.  FIG. 8  is a cross section illustrating the lens configuration of the zoom lens in Example 7. 
     The shape of the zoom lens in Example 7 is also similar to that of the zoom lens in Example 2. 
     Table 25 shows basic lens data of the zoom lens in Example 7. Table 26 shows data about the specification of the zoom lens in Example 7. Table 27 shows data about moving surface distances. Table 28 shows data about aspheric surface coefficients.  FIG. 15 , Sections A through L illustrate aberration diagrams. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 25 
               
             
             
               
                   
               
               
                 EXAMPLE 7 - LENS DATA 
               
             
          
           
               
                   
                 Ri 
                   
                 Ndj 
                   
               
               
                 Si 
                 (CURVA- 
                 Di 
                 (REFRAC- 
                 vdj 
               
               
                 (SURFACE 
                 TURE 
                 (SURFACE 
                 TIVE 
                 (ABBE 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 NUMBER) 
               
               
                   
               
             
          
           
               
                  1 
                 274.7063 
                 1.51 
                 1.83400 
                 37.16 
               
               
                  2 
                 48.1590 
                 5.78 
                 1.59282 
                 68.53 
               
               
                  3 
                 −218.7696 
                 0.10 
                   
                   
               
               
                  4 
                 47.0606 
                 4.48 
                 1.62041 
                 50.29 
               
               
                  5 
                 228.8206 
                 DD[5] 
                   
                   
               
               
                  6 
                 85.9908 
                 0.95 
                 1.88300 
                 40.76 
               
               
                  7 
                 7.8070 
                 4.23 
                   
                   
               
               
                  8 
                 −19.6274 
                 0.88 
                 1.80400 
                 46.57 
               
               
                  9 
                 128.3130 
                 0.10 
                   
                   
               
               
                 10 
                 17.7710 
                 3.41 
                 1.92286 
                 20.88 
               
               
                 11 
                 −41.2907 
                 0.88 
                 1.88300 
                 40.76 
               
               
                 12 
                 41.3492 
                 DD[12] 
                   
                   
               
               
                 13(STOP) 
                 ∞ 
                 1.50 
                   
                   
               
               
                 14 
                 8.6331 
                 4.81 
                 1.49700 
                 81.54 
               
               
                 15 
                 −15.5307 
                 0.88 
                 1.83481 
                 42.71 
               
               
                 16 
                 −55.4075 
                 0.20 
                   
                   
               
               
                 17 
                 29.1428 
                 4.51 
                 1.62041 
                 60.29 
               
               
                 18 
                 −11.0001 
                 0.88 
                 1.79952 
                 42.22 
               
               
                 19 
                 −1311.5652 
                 0.40 
                   
                   
               
               
                 *20  
                 7.3531 
                 2.50 
                 1.55864 
                 58.62 
               
               
                 *21  
                 7.7778 
                 DD[21] 
                   
                   
               
               
                 22 
                 95.1774 
                 0.80 
                 1.83400 
                 37.16 
               
               
                 23 
                 81.399 
                 0.60 
                   
                   
               
               
                 *24  
                 8.4016 
                 2.20 
                 1.53391 
                 55.89 
               
               
                 *25  
                 38.9216 
                 DD[25] 
                   
                   
               
               
                 *26  
                 2594.2187 
                 2.70 
                 1.53391 
                 55.89 
               
               
                 *27  
                 −7.5011 
                 1.10 
                   
                   
               
               
                 28 
                 ∞ 
                 0.80 
                 1.51680 
                 64.20 
               
               
                 29 
                 ∞ 
                 2.75 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 26 
               
             
             
               
                   
               
               
                 EXAMPLE 7 - SPECIFICATION (d-LINE) 
               
             
          
           
               
                   
                 WIDE ANGLE 
                 MIDDLE 
                 TELEPHOTO 
               
               
                   
               
             
          
           
               
                 ZOOM MAGNIFICATION 
                 1.0 
                 6.3 
                 38.5 
               
               
                 RATIO 
                   
                   
                   
               
               
                 f′ 
                 4.40 
                 27.70 
                 169.35 
               
               
                 FNo. 
                 3.17 
                 4.81 
                 6.31 
               
               
                 2ω[°] 
                 92.0 
                 15.2 
                 2.6 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 27 
               
             
             
               
                   
               
               
                 EXAMPLE 7 - ZOOM DISTANCE 
               
             
          
           
               
                   
                   
                 WIDE ANGLE 
                 MIDDLE 
                 TELEPHOTO 
               
               
                   
               
             
          
           
               
                   
                 DD[5] 
                 0.58 
                 41.13 
                 67.24 
               
               
                   
                 DD[12] 
                 28.75 
                 10.98 
                 2.20 
               
               
                   
                 DD[21] 
                 2.61 
                 6.52 
                 9.16 
               
               
                   
                 DD[25] 
                 2.69 
                 13.62 
                 20.59 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
           
               
                 TABLE 28 
               
               
                   
               
               
                 EXAMPLE 7 - ASPHERIC SURFACE COEFFICIENT 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 SURFACE NUMBER 
               
             
          
           
               
                   
                 20 
                 21 
                 24 
               
               
                   
               
               
                 KA 
                 0.0000000E+00 
                 0.0000000E+00 
                 9.9858849E−01 
               
               
                 A3 
                 3.5194825E−05 
                 2.4877428E−05 
                 −7.9448771E−04 
               
               
                 A4 
                 −9.1259035E−05 
                 2.7370653E−04 
                 −1.4106330E−04 
               
               
                 A5 
                 −3.4848057E−05 
                 9.7021289E−06 
                 −1.8868792E−04 
               
               
                 A6 
                 −2.8299394E−06 
                 −1.7770410E−05 
                 5.3762494E−06 
               
               
                 A7 
                 −1.6336898E−06 
                 −4.6460453E−06 
                 2.2735299E−05 
               
               
                 A8 
                 −3.6190710E−07 
                 −5.2997309E−07 
                 4.1530284E−06 
               
               
                 A9 
                 −1.0333655E−07 
                 −7.6318024E−08 
                 1.1800520E−09 
               
               
                 A10 
                 −1.2786129E−08 
                 −3.4229251E−09 
                 −4.0983097E−07 
               
               
                 A11 
                 −1.8566621E−09 
                 5.0110763E−10 
                 −8.2334264E−08 
               
               
                 A12 
                 1.8000150E−10 
                 2.3836828E−10 
                 −2.8331680E−08 
               
               
                 A13 
                 1.0931229E−10 
                 4.4141144E−11 
                 −3.1637844E−08 
               
               
                 A14 
                 2.5380661E−11 
                 7.0902347E−12 
                 3.3690565E−09 
               
               
                 A15 
                 9.4765495E−12 
                 3.2299721E−12 
                 1.1375237E−09 
               
               
                 A16 
                 2.2768029E−13 
                 7.2930789E−13 
                 2.0965110E−10 
               
               
                 A17 
                 −4.2298985E−13 
                 1.4521435E−13 
                 −1.9468436E−11 
               
               
                 A18 
                 −1.9822796E−13 
                 2.5577813E−14 
                 −5.7315055E−11 
               
               
                 A19 
                 −1.9192457E−14 
                 −4.5492169E−16 
                 1.1707052E−11 
               
               
                 A20 
                 1.0838208E−14 
                 −1.5156669E−15 
                 −8.8917300E−13 
               
               
                   
               
             
          
           
               
                   
                 SURFACE NUMBER 
               
             
          
           
               
                   
                 25 
                 26 
                 27 
               
               
                   
               
               
                 KA 
                 −3.4356281E−02 
                 −1.5919206E−02 
                 6.0897382E−01 
               
               
                 A3 
                 −3.7929976E−04 
                 3.8177383E−03 
                 5.3885518E−03 
               
               
                 A4 
                 −6.9961451E−04 
                 −1.6572658E−03 
                 −1.7916006E−03 
               
               
                 A5 
                 1.0168216E−04 
                 5.3459736E−05 
                 5.5287290E−04 
               
               
                 A6 
                 7.3843981E−06 
                 7.2602184E−05 
                 −4.3329082E−05 
               
               
                 A7 
                 −1.6226768E−06 
                 −4.8974929E−06 
                 −9.9407611E−06 
               
               
                 A8 
                 2.0881076E−07 
                 −1.8692134E−06 
                 1.1038055E−06 
               
               
                 A9 
                 3.1749046E−07 
                 1.5162102E−08 
                 3.1755849E−07 
               
               
                 A10 
                 2.7569861E−07 
                 5.9534773E−08 
                 3.0676327E−08 
               
               
                 A11 
                 2.8387925E−08 
                 9.1638701E−09 
                 −2.3009594E−09 
               
               
                 A12 
                 6.0966231E−09 
                 5.7322777E−10 
                 −1.1315956E−09 
               
               
                 A13 
                 −3.9007838E−09 
                 −2.0838522E−10 
                 −1.8971726E−10 
               
               
                 A14 
                 −4.4058901E−09 
                 −7.7327336E−11 
                 −1.2784100E−11 
               
               
                 A15 
                 −6.7430841E−10 
                 −1.3480473E−11 
                 1.9511726E−12 
               
               
                 A16 
                 4.6896009E−11 
                 −2.8760743E−13 
                 −5.4179089E−14 
               
               
                 A17 
                 −5.3144357E−12 
                 3.0669242E−13 
                 −3.9170140E−14 
               
               
                 A18 
                 7.7085581E−11 
                 1.2921973E−13 
                 1.9739940E−14 
               
               
                 A19 
                 −2.4348533E−12 
                 1.5038695E−14 
                 1.8928268E−14 
               
               
                 A20 
                 −2.8770423E−12 
                 −4.6753424E−15 
                 −2.5889239E−15 
               
               
                   
               
             
          
         
       
     
     Table 29 shows values corresponding to conditional expressions (1) through (10) for the zoom lenses in Examples 1 through 7. In all of the examples, d-line is a reference wavelength. The following Table 29 shows values at this reference wavelength. 
     
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 29 
               
               
                   
               
               
                 EXPRESSION 
                 CONDITIONAL 
                 EXAMPLE 
                   
                   
                   
                   
                   
                   
               
               
                 NUMBER 
                 EXPRESSION 
                 1 
                 EXAMPLE 2 
                 EXAMPLE 3 
                 EXAMPLE 4 
                 EXAMPLE 5 
                 EXAMPLE 6 
                 EXAMPLE 7 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 (1) 
                 Nd11 
                 1.834 
                 1.904 
                 1.804 
                 1.911 
                 1.911 
                 1.834 
                 1.834 
               
               
                 (2) 
                 νd11 
                 37.16 
                 31.32 
                 39.60 
                 35.25 
                 35.25 
                 37.16 
                 37.16 
               
               
                 (3) 
                 νd12 
                 70.23 
                 81.54 
                 81.54 
                 81.54 
                 81.54 
                 68.63 
                 68.63 
               
               
                 (4) 
                 |f2|/ft 
                 0.0397 
                 0.0392 
                 0.0389 
                 0.0341 
                 0.0303 
                 0.0481 
                 0.0468 
               
               
                 (5) 
                 νd2p 
                 17.98 
                 20.88 
                 18.90 
                 17.98 
                 17.98 
                 20.88 
                 20.88 
               
               
                 (6) 
                 νd13 
                 60.64 
                 68.63 
                 68.63 
                 53.87 
                 63.33 
                 60.29 
                 60.29 
               
               
                 (7) 
                 νd3pc 
                 81.54 
                 81.54 
                 70.23 
                 81.54 
                 81.54 
                 81.54 
                 81.54 
               
               
                 (8) 
                 f1/|f2| 
                 11.296 
                 12.657 
                 11.965 
                 12.731 
                 13.239 
                 11.911 
                 11.092 
               
               
                 (9) 
                 |f4|/(fw × ft) 1/2   
                 0.607 
                 0.710 
                 0.694 
                 0.632 
                 0.613 
                 0.523 
                 0.885 
               
               
                 (10) 
                 f5/|f4| 
                 0.737 
                 0.666 
                 0.665 
                 0.701 
                 0.682 
                 0.987 
                 0.580 
               
               
                   
               
             
          
         
       
     
     As these data show, all of the zoom lenses in Examples 1 through 7 satisfy conditional expressions (1) through (10). It is recognizable that the size of the zoom lenses is small, and various aberrations are excellently corrected while the zoom lenses have high variable magnification ratios. 
     Next, an imaging apparatus according to an embodiment of the present invention will be described.  FIG. 16  is a schematic diagram illustrating the configuration of an imaging apparatus using a zoom lens according to an embodiment of the present invention, as an example of an imaging apparatus according to an embodiment of the present invention. In  FIG. 16 , each lens group is schematically illustrated. This imaging apparatus is, for example, a video camera, an electronic still camera or the like using a solid state imaging device, such as a CCD and a CMOS, as a recording medium. 
     An imaging apparatus  10  illustrated in  FIG. 16  includes a zoom lens  1 , a filter  6  having a function of a low-pass filter or the like, and which is arranged toward the image side of the zoom lens  1 , an imaging device  7  arranged toward the image side of the filter  6 , and a signal processing circuit  8 . The imaging device  7  converts an optical image formed by the zoom lens  1  into electrical signals. For example, a CCD (Charge Coupled Device), a CMOS (Complementary Metal Oxide Semiconductor) or the like may be used as the imaging device  7 . The imaging device  7  is arranged in such a manner that an imaging surface of the imaging device  7  is matched with the image plane of the zoom lens  1 . 
     An image imaged by the zoom lens  1  is formed on the imaging surface of the imaging device  7 , and signals about the image are output from the imaging device  7 . Operation processing is performed on the output signals at a signal processing circuit  8 , and an image is displayed on a display device  9 . 
     So far, the present invention has been described by using embodiments and examples. However, the present invention is not limited to the aforementioned embodiments nor examples, and various modifications are possible. For example, the values of a curvature radius, a distance between surfaces, a refractive index, an Abbe number and the like of each lens element are not limited to the values in the aforementioned numerical value examples, and may be other values.
A zoom lens consists of a first lens group having positive refractive power, a second lens group having negative refractive power, a third lens group having positive refractive power, a fourth lens group having negative refractive power, and a fifth lens group having positive refractive power in this order from an object side. Distances between the lens groups change during magnification change, and the first lens group is positioned closer to the object side in a telephoto end state than its position in a wide angle end state. Further, the first lens group consists of three lenses of an 11th lens having negative refractive power, a 12th lens having positive refractive power and a 13th lens having positive refractive power in this order from the object side. Further, the following conditional expressions are satisfied:
 
1.75&lt;Nd11  (1);
 
28&lt;νd11&lt;44  (2);
 
63&lt;νd12  (3); and
 
0.020&lt;| f 2|/ ft &lt;0.050  (4).