Key concepts
Mathematics
Patterns
Interference
Optical illusion

Introduction
Have you ever wondered why our eyes are drawn to patterns? We see patterns in art and music, and also in our daily lives. Patterns can provide a sense of order and can make a hectic-looking world a little more manageable. They are the basis of many assumptions and predictions. We assume we will have lunch at noon if that is what we always do. We predict thunderclouds will bring rain. And you might expect to get in trouble when you disobey the rules.

We are so used to looking for patterns that we might even see one where there is none. In this activity we look for one of those illusions: one that printers avoid but scientists have put to good use.

Background
Sometimes the whole is more than the sum of its parts. This is definitely true with interference patterns, which are the result of waves intersecting in a constructive or destructive way. In acoustics interference of two waves with slightly different frequencies creates a beat, or a periodic variation in volume. In optics the double-slit experiment showed the interference of two slightly displaced light waves of the same frequency gives rise to a series of alternating dark and bright bands. A lesser-known interference pattern—the moiré interference pattern—occurs when a regular pattern with transparent gaps overlaps another similar pattern. The two patterns must almost exactly overlap or be almost identical. A small displacement, rotation or difference in period, etcetera, is essential for the interference pattern to occur.

Moiré patterns are the enemy of many: In printing arrangements of dots can create unwelcome moiré patterns; in television and digital photography a pattern on an object can interfere with the pattern of the light sensors or camera sensors, adding unwanted moiré patterns to the picture. Scientists, on the other hand, have managed to use moiré patterns to their advantage in tools to make microscopic measurements. Moiré patterns are attractive there because the periodicity of the created pattern magnifies the tiny differences of the interfering patterns.

Materials

• Pocket combs (At least two should be identical or have pins that are almost identical in thickness and spacing.)
• Two screens, such as window screens, at least one of which you can manipulate freely
• Nylon stockings
• Surface or background that is a contrasting color to your materials to help spot the patterns

Preparation

• Gather your materials together in your work space.

Procedure

• Start with the pair of combs. Place them separately on a contrasting background. How would you describe the pattern of pins? Is it regular or irregular? Are the pins spaced far apart or close to one another?
• If you place two identical combs exactly on top of each other so they perfectly overlap, how do you expect the pattern of pins you observed to change? Would it be any different if you make the two combs almost perfectly line up?
• Test your prediction. If you do not have two identical combs, use two that are very similar in their pin patterns. Do you see what you predicted?
• If the combs are slightly misaligned or if their pattern of pins is slightly different, you should see a third pattern occur: one that has a distance between repeating parts than is several times the distance between the individual pins of the combs. If you cannot see it, try a different combination of combs or switch the top comb with the bottom one. Having a contrasting background can help as well.
• Shift the top comb slowly side to side. What do you observe now?
• Rotate the combs over a small angle with respect to each other. Does the pattern change? What happens if you increase the angle of rotation? (Hint: Pay attention to the distance between the repeated parts of the appearing pattern.)
• Test different combinations of combs to find out what is necessary to make these patterns appear.
• You just explored overlapping patterns of parallel lines. Do you think the same thing would happen if you overlapped other patterns such as patterns of squares?
• Look at a window screen. Do you see the pattern of squares? Notice that the size of a square determines the distance between the repeating parts of this pattern.
• Observe a second window screen. Does it have squares of a similar size?
• Think for a moment. How would you place the two screens together to create a third pattern? Think about how this is similar and how it is different from your comb experiment.
• If you can, try it out. Does a new pattern appear?
• How do the patterns change when you change the angle of rotation between the screens?
• Imagine shrinking the squares in the window screen until they are tiny. Would it almost look like looking through a single layer of nylon stocking? Do you think you can create patterns by overlapping layers of nylon stockings? Why or why not?
• Perform the test. Look through two layers of nylon against an even, contrasting background. Do you see patterns occur? How are they similar and how are they different from the patterns you saw earlier?
• Extra: What you observed in this activity are moiré patterns. Can you find other moiré patterns around the house, such as folded thin curtains or, when outside, driving or walking around town? Pay attention to chain-link fences. The fence and its shadow can even combine to create a moiré pattern. Watch how the patterns change as you move.
• Extra: Use a computer printer and print identical patterns of lines or concentric circles on two transparencies. Can you create artistic moiré patterns by shifting or rotating these transparencies with respect to each other?
• Extra: Use an online moiré pattern generator to create some nice patterns. Try to predict how the pattern will change when you change one of the parameters.

Observations and results
Did you see patterns appear when two identical (or almost identical) repetitive patterns overlapped? Did the distance between repetitive parts decrease as you increased the angle of rotation?

The appearing patterns are called moiré patterns. They amplify small differences between two identical or almost identical repetitive patterns. If you had identical combs and could exactly line them up, no moiré pattern should have been visible. It is the small differences in pattern or the small misalignment that gives rise to clearly visible longer-range moiré patterns. Did you notice that an increase in misalignment—a larger shift, a larger angle of rotation or a bigger difference in initial patterns—made the distance between repetitive parts in the moiré pattern decrease? Once the differences in the two initial patterns or the misalignments are too big you can no longer detect the moiré pattern.

Moiré patterns are not really there; they are an optical illusion created in the image in your eye.

More to explore
Optical Illusions: Moiré Pattern Generator, from Molecular Expressions
Double-Slit Science: How Light Can Be Both a Particle and a Wave, from Scientific American
Shadow Bands During a Total Solar Eclipse, from Strickling.net
Spooky Science: Make a Ghostly Illusion, from Scientific American

This activity brought to you in partnership with Science Buddies