# An Infinite Number of Reflections? Really?

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## Summary

Key Concepts
Reflection, mirrors, light, infinite number
Credits
Sabine De Brabandere, PhD, Science Buddies

## Introduction

Can you imagine a bouncy ball bouncing back and forth between two walls, infinitely?  Wouldn’t that be amazing?

What if, instead of a ball, light was bouncing between two mirror walls; would it bounce back and forth forever?  Imagine each light bounce added one reflection of you in the mirror; would it look like there were an infinite number of “you’s” in there?  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’ll be inspired to create some real works of beauty.

This activity is not recommended for use as a science fair project. Good science fair projects have a stronger focus on controlling variables, taking accurate measurements, and analyzing data. To find a science fair project that is just right for you, browse our library of over 1,200 Science Fair Project Ideas or use the Topic Selection Wizard to get a personalized project recommendation.

## Background

The reason why you see objects is because some light hitting these objects reflects back into your eyes. But what happens if light coming from an object hits a flat mirror and is reflected (or bounced back) before it hits your eyes? Your brain, being unaware that the light was reflected, will reconstruct an image with the information it received, assuming the light traveled on a straight path from the object to the eye. The result is what you see in the mirror: an object that looks similar, but appears to be placed behind the mirror. We call this a reflection of the object. It is an optical illusion, a virtual image of a real object.

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 vaguer than the image made with the same light reaching the eye directly.

Now, what image would your brain create if light reflected several 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: Nail polish or watercolor marker
• Optional: Trinkets or other small, colorful objects

## Preparation

1. Optional: To make observing easier, you could choose to color the nail of your left-hand index finger (right hand if you are left-handed) with nail polish or a watercolor marker. Watercolor markers wash off easily.

## Instructions

1. Stand in front of a large wall mirror, looking into the mirror. Make sure there are about twenty centimeters between you and the mirror.
2. Hold a small mirror just under your eyes, such that the reflective surfaces of the mirrors are facing each other.
3. Place your index finger (the painted one, if you chose to do that step) between the two mirrors, with your fingernail facing the large wall mirror. Do you see the reflection of your finger in the wall mirror? Do you see the nail, the skin-side of your fingertip or both?
4. Keep looking at your index finger in the large wall mirror and remove the small mirror and put it back again. Is what you see in the wall mirror different when you hold the small mirror in place? How is it different? Can you explain what you see?
5. Tilt the small mirror a little and watch what happens to the reflection(s). Is there a particular position in which you can see very few reflections? What is the fewest number of reflections you see? And is there a position in which you can see a lot of reflections? How many can you see? Do they seem to go on forever?
6. Hold your small mirror in a position in which you see a lot of reflections. Do you get the impression that reflections are farther and farther away? How are reflections that appear to be far away different from the reflections that appear to be close? Do they get dimmer, less sharp?
7. Take a step back from the wall mirror, being careful not to step into objects behind you. How does your image change if there is more space between the two mirrors? Now get very close to the wall mirror. Which distance results in more reflections?

Extra: Hold your small mirror vertically against the large mirror, at a ninety 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 ninety 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 you see the wall mirror and small mirror at the same time. How many reflections do you see this time? Reduce the angle between the two reflective surfaces to close to 60 degrees. How many reflections do you see this time?  Repeat with 45 degrees and 30 degrees. Do you see a pattern? Can you explain what you observe?

Extra: Use the reflection properties you just explored and some other colorful objects, like 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. Can you explain how it works? How many mirrors do you think your kaleidoscope contains? At what angle do you think the mirrors are placed? Ask permission to take the kaleidoscope apart, informing the owner or your parents that you might not be able to put it back together nicely. You can also invest in 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.  How does the resulting image change if you cover one mirror with black construction paper? How does it look when you cover more mirrors? What happens when you leave the eyepiece off (the piece where you look through)? Try taking off the piece containing the little trinkets and cover the tube with a colorful drawing. Do you see anything? Lift the tube a little, does an image appear? Why do you think this happens?

## Observations and Results

Did you get the impression of an infinite series of fingers?

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 list. The reflections in your activity probably looked as if they went on and on, an infinite number of times.

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 some reflections, the image fades out and you are no longer able to distinguish reflections. Increasing the distance between the mirrors will generate a faster fading, and thus, result in less 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 when you held one mirror against another at a ninety degree angle or at a smaller angle, you should have seen a circle of images appear. When the angle is an even division of three hundred sixty degrees (a full circle) you will get a beautiful pattern of reflections.  Kaleidoscopes use both—the apparent infinite reflections and the mirrors at an angle—to create beautiful images.