(30 minutes or less)
If you start with one large piece of mirror, cut three 6 x 6 inch (15 x 15 cm) pieces from the plastic or glass. You can cut the plastic with a fine saw, such as a hacksaw, or score it with a utility knife and then snap it off. It is not hard to cut glass; get someone who knows how to do it to show you. (WARNING: For safety, after cutting a glass mirror, mount it on wood or cardboard and cover the edges with duct tape.)
Once you have the three mirrors you need, use the duct tape to tape two of the mirrors together along one edge. Put the tape on the back side of the mirror, making a hinge that opens and closes easily. Be sure the mirrors can move freely from 0 degrees to 180 degrees.
(15 minutes or more)
To make a kaleidoscope, set the hinged mirrors on the cardboard, and place an object such as a pencil or some coins between them. Open the mirrors to different angles. Notice that the smaller the angle, the greater the number of images you see. Remove the objects and see what happens when you draw different designs in the space between the two mirrors.
Close your right eye and look at a single mirror straight on. Notice that the left eye of the image is closed. Now close your right eye and look at two mirrors that form a 90-degree angle. Notice that the right eye of this image is closed.
Now make a corner reflector by opening the two taped mirrors to 90 degrees and resting them on the third mirror, so that the three mirrors form a half cube (see diagram). Close one eye and stare right at the corner where the three mirrors join. Move your head and notice that the pupil of your open eye always falls right at the corner. Open both eyes and look at the corner. One eye may appear to be closer to the corner than the other. This is your dominant eye.
When you put an object between the two hinged mirrors, light from the object bounces back and forth between the mirrors before it reaches your eyes. An image is formed each time the light bounces off a mirror. The number of images that you see in the mirrors depends on the angle that the mirrors form. As you make the angle between the mirrors smaller, the light bounces back and forth more times, and you see more images.
The illustration below shows how an image is formed in the corner of two mirrors at 90 degrees. Light rays bounce off each mirror at the same angle that they hit the mirror: Physicists say that the angle of reflection is equal to the angle of incidence. Mirrors at other angles behave similarly, but the ray diagrams may get more complex.
The inside corner of a corner reflector (where the three mirrors meet) sends light back parallel to its original path. If you pointed a thin beam of laser light right near the corner, the beam would bounce from mirror to mirror and then exit parallel to the entering beam. Light from the center of your eye bounces straight back to the center of your eye, so the image of your eye seems to be centered in the corner made by the mirrors.
In a corner reflector, multiple reflections reverse the image and invert it.
Corner reflectors are used to make safety reflectors for cars, bicycles, and signs. Corner reflectors have also been used to bounce laser beams back to the earth from the surface of the moon.
Throw a tennis ball into the corner of a room. It should return to you after bouncing off the three surfaces.
Tape five square mirrors together with the mirrored surfaces facing inward to form a box. Place a sixth mirror, turned at a 45-degree angle, over the open side so you can look into the box and also let some light in. This combines the Look into Infinity Snack with this Corner Reflector Snack. Try other configurations of mirrors in three dimensions and see what you can discover.
To do a quantitative experiment, mark the following angles on a piece of cardboard: 180 degrees, 90 degrees, 60 degrees, 45 degrees, 36 degrees, 30 degrees, and 20 degrees. These angles are chosen so that when they are divided into 360 degrees they produce an even integer. Mount the hinged mirrors at each of these angles and place an object betvveen them. Count the number of images you see. You should be able to verify the following rule: 360 divided by the angle between the mirrors gives the number of images, plus one. At 60 degrees, for example, 360/60 = 6, so you should see five images of the object.