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# Multiple Reflections – Introduction and Explanation

Aug 20, 2022

## Multiple Reflections

### Key Concepts

• Seeing behind oneself
• Formation of multiple images
• Multiple reflections
• Periscope

### Introduction

A mirror forms an image of an object placed in front of it, as a result of the reflection of light emerging from the object. The same set of reflected rays can reflect off multiple times from mirrors to produce multiple images of the same object. This technique can be used in many ways. In this section, we will be looking at multiple reflections and its applications.

### Seeing behind oneself:

A person usually cannot turn their head enough to see behind themselves. However, it is possible to see behind oneself by using two mirrors. One at the front and the other at the back, if one intends to see their backside.

For example, in the first picture given below, Rihana is able to see her braided hair which lie at her back by placing a mirror in front of her and an additional mirror behind herself. And in the second picture, Kelvin is able to see a note stuck to his back by placing a mirror in front of him and an additional mirror behind himself.

This is possible as the light from the source in the room falls on the back of Rihana’s head. It reflects off her head onto Katie’s mirror. It again reflects off Katie’s mirror onto the mirror in front of Rihana. It then reflects off the mirror in front of Rihana into her eyes. As a result, Rihana could see her braids lying at the back of her head.

In the same way, the light from the source in the room falls on the back of Kelvin’s head. It reflects off his back onto the mirror at his backside. It again reflects off the mirror in his backside onto the mirror in front of Kelvin. It then reflects off the mirror in front of Kelvin into his eyes. As a result, Kelvin could see the sticky note lying at his back.

### Multiple Reflections:

Take two rectangular plane mirror pieces (without frame) and arrange them at some angle in an upright position. Place a lighted candle in the middle of the two mirror pieces.

The number of images that are seen in the mirrors depends upon the angle between the two mirrors.

Let the angle between the mirrors be A. Then the number of images formed n is given by,

The above formula can be used to work out the number of images of the object that is formed for a particular angle between the mirrors.

When we place the mirrors side by side, they behave like a single mirror. Hence, only one image of the candle is formed.

#### Case 1: A = 180 degrees

Now, the angle between the mirrors is A = 180 degrees.

Thus, the number of images n is given by,

n = 2 – 1 = 1

n = 1

Thus, the formula also yields the same result.

#### Case 2: A = 120 degrees

Or,

Or, n = 3 – 1

Or, n = 2

When the mirrors are inclined at an angle of 120 degrees, 2 images of the lighted candle are formed.

#### Case 3: A = 90 degrees

The number of images,

Or,

Or, n = 4 – 1

Or, n = 3

When the mirrors are inclined at an angle of 90 degrees, 3 images of the lighted candle are formed.

#### Case 4: A = 72 degrees

The number of images,

Or,

Or, n = 5 – 1

Or, n = 4

When the mirrors are inclined at an angle of 72 degrees, 4 images of the lighted candle are formed.

#### Case 5: A = 60 degrees

The number of images,

Or,

Or, n = 6 – 1

Or, n = 5

When the mirrors are inclined at an angle of 60 degrees, 5 images of the lighted candle are formed.

#### Case 6: A = 45 degrees

The number of images,

Or,

Or, n = 8 – 1

Or, n = 7

When the mirrors are inclined at an angle of 45 degrees, 7 images of the lighted candle are formed.

#### Case 7: A = 30 degrees

The number of images,

Or,

Or, n = 12 – 1

Or, n = 11

When the mirrors are inclined at an angle of 30 degrees, 11 images of the lighted candle are formed.

#### Case 8: A = 0 degrees

(The two mirrors are placed parallel to each other)

The number of images,

Or,

Or, n = infinite

When the mirrors are inclined at an angle of 0 degrees, infinitely many images of the lighted candle are formed.

The results of the above calculations are listed in the table below.

### Periscope:

A periscope is an optical device that helps us to see over the top of something. They are used to see objects that are not at the same level as that of the observer. Submariners use it to see what is on the surface of the sea. People also use it to see above an obstacle such as the heads of the people in front of them or a wall.

In a periscope, there are two mirrors placed parallel to each other. These two mirrors are placed at an angle of 45 degrees to the horizontal. The light from the object falls on mirror 1, gets reflected and falls on mirror 2, and then reflects off mirror 2 to reach the eyes of the observer.

## Summary

1. One can see behind themselves by placing a mirror in the front and another mirror in the back.

2.When two mirrors are placed in an upright position side by side forming an angle between them, the number of images they produce for an object placed in the middle depends on the angle between them.

3. The number of images increases from 1 to infinity when the angle between the mirrors decrease from 180 to 0.

4. The number of images formed is related to the angle between the mirrors as

5. A periscope is an optical device which helps us to see over the top of something. They are used to see the objects that are not at the same level as that of the observer.

6. Periscopes are used in submarines to see what is happening on the surface of the water.

7. Periscopes contain two mirrors placed parallel to each other and inclined at an angle of 45 degrees with the horizontal.

8. These two mirrors reflect light coming from the object to be viewed one after the other to make it visible to the observer.

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