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Look Into Infinity

Science Snack
Look Into Infinity
Images of images of images can repeat forever.
Look Into Infinity
Images of images of images can repeat forever.

If you've ever been between two mirrors that face each other, such as in a barbershop or a beauty salon, you're familiar with the seemingly endless line of images fading into the distance. This Snack recreates this effect.

Note: This activity can be done with glass mirrors, but we highly recommend using plastic acrylic mirror because it's much safer. If you must use glass, tape the edges to prevent cuts and glue the entire surface to a backing of cardboard or wood to minimize loose shards of glass flying if the mirror cracks or breaks. It's also not practical to make a hole in a glass mirror, but you can look over the top of one mirror to get the same effect. You can even simulate a hole by very carefully scraping away a small area of the silver backing.

Tools and Materials
  • Two square pieces of acrylic plastic mirror, available from plastics stores (mirrors shown in the photo are 9 inches [23 cm] per side, but exact size is not critical); have the plastic store drill a 1-inch (2.5-cm) hole in the center of one of the pieces—you can get the effect without the hole, but the hole gives a more interesting perspective
  • Some kind of stand (see Assembly section below)
  1. Position the mirrors so that their reflecting surfaces are facing each other and are parallel. The mirrors can be anywhere from a few inches to a foot apart.
  2. Make mirror stands. You can use wood and hot glue as shown in the photo. An even simpler alternative is to place a full soda can (or any suitably heavy object) on each side of a mirror to support it. Or feel free to devise your own stands!
To Do and Notice

With the reflecting surfaces facing each other, look through the hole into the space between the mirrors. (If you didn’t make 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 the 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 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.

What's Going On?

Light rays are reflecting from both the front of the object and from the back of the object. After the first reflection, you see one image in each mirror: a front-side image in one mirror and a back-side image in the other. After the second reflection, you see a second image in each mirror, then a third, and so on.

As you look at the images formed in one of the mirrors, 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. 

Going Further

An interesting handheld variation of this Snack involves gluing the two mirrors to a block of foam rubber, which acts as a spacer. Mirrors 6 × 6 inches (15 × 15 cm) work well for this portable version, but mirror size is not crucial. The foam should separate the mirrors by 2 or 3 inches (5 to 8 cm).

An even simpler handheld version 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. See the diagram below (click to enlarge).

Squeeze the foam or sponge so the mirrors are not quite parallel to each other, and you’ll see a pattern of images that curves off into infinity!

As you can see in the diagram, another version of this Snack involves making two holes in one of the mirrors—one for each eye. Try it!