(15 minutes or less)
Cut a hole about 1 inch (2.5 cm) in diameter near the center of one of the mirrors. You can use a hole saw, or you can have this done for you at the plastics store. You can get the effect without the hole, but the hole gives a more interesting perspective. If you don't care about the hole, you can use glass mirror tiles instead of a plexi-mirror. You can even create the hole on a glass mirror tile by scraping away the silver backing.
Stand the mirrors so that their reflecting surfaces face each other and are parallel to each other. The mirrors can be anywhere from a few inches to a foot apart. You can make a wooden stand for each mirror by cutting a slit along the length of the flat side of a piece of 1 x 4 inch (2.5 x 10 cm) pine. Then slip the mirror into the slit. You can also stand each mirror between two pieces of wood held together by rubber bands, or place two full softdrink cans (or any heavy objects) so that one is on each side of the mirror, supporting it.
(5 minutes or more)
With the reflecting surfaces facing each other, look through the hole into the space between the mirrors. (If you didn't bother making a hole, just look over the top of one mirror.) You can also try placing either your finger or some other object between the mirrors.
If you place an object between the mirrors, notice that there is a repetitious pattern in the orientation and spacing of the images. Objects with contrasting colors on the front and back (such as red and white) show this well. Successive images alternate from front view to back view. If the original object is closer to one mirror than to the other, the distance between successive images will alternate from close together to far apart - making the images seem to be grouped in pairs, with a front side always facing a front side, or a back side always facing a back side.
In this light-ray diagram, the solid lines show the actual path of the light rays; the dashed lines show the path of the light rays projected by your brain. You see images where the dashed lines come together.
This light-ray diagram shows the rays that come from the front of an object and those that come from the back. After the first reflection, you see one image in each mirror where the dashed lines come together (1). After the second reflection, you see a second image in each mirror (2), and so on.
As you look at the images formed in one of the mirrors on the diagram, notice that there is an alternation of front and back views, that the images appear to be grouped in pairs, and that a front side is always facing a front side and a back side is always facing a back side. This corresponds to what you actually observe in the mirrors.
An interesting variation on the version described involves gluing the two mirrors to a block of foam rubber. Mirrors 6 x 6 inches (15 x 15 cm) work well for this handheld portable version, but mirror size is not crucial. The foam should separate the mirrors by about 2 to 3 inches (5 to 8 cm).
An even simpler handheld version of this Snack uses pieces of sponge as spacers, with rubber bands holding the mirrors together. Use a soft sponge. The cheap ones used for washing cars work well. One or two holes can be drilled into the mirror.
Squeeze the foam so that the mirrors are not quite parallel to each other. You will see a pattern of images that curves off into infinity. Try it, you'll like it!
And if you enjoyed that one, why not take a look at the Corner Reflector Snack?