Angle of view camera–subject distance to preserve the size of a subject, changing the angle of view can indirectly distort perspective, changing the apparent relative size of the subject and foreground. If the subject image size remains the same, then at any given aperture all lenses, wide angle and long lenses, will give the same depth of field. An example of how lens choice affects angle of view. This table shows the diagonal, horizontal, and vertical angles of view, in degrees, for lenses producing rectilinear images, when used with 36 mm × 24 mm format (that is, 135 film or full-frame 35mm digital
Octagon "S" is the span of the octagon, or the second-shortest diagonal; and "a" is the length of one of the sides, or bases. This is easily proven if one takes an octagon, draws a square around the outside (making sure that four of the eight sides overlap with the four sides of the square) and then takes the corner triangles (these are 45–45–90 triangles) and places them with right angles pointed inward, forming a square. The edges of this square are each the length of the base. Given the length of a side "a", the span "S" is The area