IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

# Multiple Images with Plane Mirrors

## Introduction

The number of images formed by two adjacent plane mirrors depends on the angle between the mirror. If $$\theta$$ (in degrees) is angle between the plane mirrors then number of images are given by,

\begin{align} n=\frac{360}{\theta}-1. \end{align}

We verify this formula in this experiment.

## Apparatus

Two plane mirrors, protractor to measure angle, candle, matchbox.

## Procedure

Take two plane mirrors (without frame). Place both the mirrors side by side and fix the junction where they meet with a cello tape. Now you will be able to open and close the mirrors like a book. Place both the mirrors at a small angle apart in the upright position on the floor. Place a lighted candle in the space between the two mirrors. You will observe many images of the candle which makes a beautiful scene.

Now, by gradually decreasing the angle between the mirrors observe the images being formed. You will now observe more and more numbers of images of the candle. Similarly, if the angle between the mirrors is increased the number of images decreases and when this angle is 180 degree, only one image is visible.

When the angle between the two mirrors is 180 degree they together act like a single mirror so that only one image is visible. As the angle between the mirrors gradually decreased, not only the candle but the mirrors themselves get imaged in one another. That is why when the angle between the mirrors is decreased one observe image within image, and image within that image, and so on. In this way one observes a lot many images. If the angle between the mirrors is finally decreased to zero, infinite images are expected to be formed.

1. Place both the mirrors vertically with 180 degree angle between the them.
2. Place a lighted candle in the space between the two mirrors.
3. You will see single image of the candle in mirror. Reduce the angle between mirrors and observe multiple images of the candle which makes a beautiful scene.
4. Now, measure the maximum angle between two mirrors when you get 1, 3, 5, 7, and 9 images. These angles are $$\theta_\text{measured}$$.
5. Calculate $$\theta_\text{calculated}$$ for $$n=1,3,5,7,9$$ by using the formula given above.
6. Draw the ray diagram when angle between two mirrors is 90 degree.

## Discussion

$$n$$ $$\theta_\text{measured}$$ $$\theta_\text{calculated}$$ $$\Delta\theta_\text{error}$$
1
3
5
7
9

## Note

Fill a transparent glass tray with water and fix two similar mirrors at its opposite ends. See the image being formed. What you see is a very long water canal. Think how this happens?

This setup is also used to make a funny game. Make a cap with two strips of different colors (say black and white) pasted on the left and the right side. Adjust the angle between the mirrors so that you see two images of yourselves (with cap and strips clearly visible). Ask your friend to wear the cap and see his image in the mirrors. Order him to touch the white or black strip quickly. There is a great chance that your friend gets confused and end up touching wrong color strip. Why this happened?