In a corner reflector, multiple reflections reverse the image and invert it.
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 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 (click to enlarge) 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.
For another way to use this Snack, 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. Try other configurations of mirrors in three dimensions and see what you can discover.
To do a quantitative experiment, use a protractor to 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 between 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, minus one, gives the number of images. At 60 degrees, for example, (360/60)–1 = 5, so you should see five images of the object.