Can You Create an Infinite Number of Reflections?

How many reflections can you make? With just a couple of mirrors--and the correct angles--you see (almost) forever. Learn how this optical trick works, and try it out at home!

Key conceptsMirrorsInfinity

Introduction

What if, instead of a ball, light was bouncing between two walls, which were both covered in mirrors? Do you think could bounce back and forth forever? Imagine each light bounce added one reflection of an object in the mirror—for example, you! Would it look like there were an infinite number of "yous"? Perhaps you have noticed something like this in a fun house or a room with multiple mirrors. But can we create an infinite number of reflections?

Try this activity, and be amazed by the many images mirrors can create! Before you know it, you might be inspired to create some real works of beauty.

Background

Mirrors, being shiny, reflect almost all the light hitting their surface. In addition, they have a very smooth surface, causing light to reflect in an orderly way. This allows your brain to reconstruct a clear image. High-quality mirrors reflect light especially well, but even high-quality mirrors absorb and scatter a small fraction of the light hitting them. As a result, a reflection is always a little dimmer and slightly less crisp than the image made with the same light reaching the eye directly.

Now, what image would your brain create if light reflected times before hitting your eyes? Find out in this activity, and discover ways to create beautiful images!

Materials

• Large wall mirror
• Small mirror with thin or no border
• Optional: trinkets or other small, colorful objects

Preparation

• Collect your small mirror along with any colorful objects you might wish to use.

Procedure

• Stand in front of a large wall mirror, looking into it. Make sure there are about twenty centimeters between you and the mirror.
• Hold a small mirror just under your eyes, so that the reflective surfaces of the mirrors are facing each other.
• Place your index finger between the two mirrors, with your fingernail facing the large wall mirror.
• While looking at your index finger in the large wall mirror, briefly remove the small mirror and then put it back again.
• Tilt the small mirror a little and watch what happens to the reflection(s).
• Hold your small mirror in a position that allows you to see a lot of reflections.
• Take a step back from the wall mirror. Now get very close to the wall mirror.
• Extra: Hold your small mirror vertically against the large mirror, at a 90-degree angle. It might help to rest the small mirror on a flat surface placed next to the wall mirror. Place your fingertip or a small, colorful object somewhere in the 90-degree angle between the two reflective surfaces. Level your eyes with the small mirror and look toward the vertical line where the two mirrors touch, so that you see the wall mirror and small mirror at the same time. Reduce the angle between the two reflective surfaces to close to 60 degrees. Repeat with angles of 45 degrees and 30 degrees.
• Extra: Use the reflection properties you just explored and some other colorful objects, such as beads or other trinkets, to make a work of beauty. Then try to draw your creation and note the symmetry.
• Extra: If you have a kaleidoscope, look through it. ? If you are allowed, you could try taking the kaleidoscope apart (knowing that you might not be able to return it to its original condition). (You can also use a kaleidoscope-making kit.) If you can take it apart, do so and explore the inside of the kaleidoscope. Then put it back together, changing one item at a time, and watch the result. Try removing the piece containing the little trinkets and cover the tube with a colorful drawing.

Observations and results

When you looked at your finger in the wall mirror, you saw a reflection created by light bouncing off your finger hitting the mirror surface and reflecting back in your eyes. The finger appeared to be behind the mirror. Did you notice that you saw the side of your finger facing the mirror, the nail side?

When you added the small mirror, you allowed light that was reflected on the wall mirror to hit the small mirror. This created a reflection of a reflection. You could not see this reflection of a reflection, as it was created behind the small mirror while you were looking in the wall mirror. However, you could observe a reflection of it as light from the reflection of a reflection hit the wall mirror and bounced back. A small fraction of this bounced-back light reached your eye, allowing you to see the reflection of a reflection of a reflection. Each bounce of light, back and forth, will add another reflection of a reflection to the count. The reflections in your activity probably looked as if they went on and on an infinite number of times (although given what we know about mirrors scattering and absorbing some of the light each time, we know that the number we could see is actually finite).

Did you notice that the small mirror also reflected the skin-side of your fingertip, so you could see the skin-side of your fingertip as a reflection of a reflection in the wall mirror?

Did your reflections get dimmer and less sharp as they appeared to be farther away? With each reflection, the mirror absorbs and scatters a tiny fraction of the light. After several reflections, the image fades out and you are no longer able to distinguish reflections. Increasing the distance between the mirrors will accelerate this fading, and thus, result in fewer visible reflections.

You might have been able to block reflected light with your finger, preventing any further reflections to occur. In this case, you only saw one reflection showing your fingernail.

When you tried the extra activity, holding one mirror against another at a 90-degree angle or at a smaller angle, you should have seen a circle of images appear. When the angle is an even division of 360 degrees (a full circle) you will get a beautiful pattern of reflections. Kaleidoscopes use both—the seemingly infinite reflections and the angled mirrors—to create beautiful images.

More to exploreThe Reflection of Light, from Optics 4 KidsSight-Line Science: Candle in the Mirror, from Kaleidoscope Science, from Science Buddies

Science Buddies

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