Question

Find the angle at which two plane mirrors should be placed to obtain three images of a single object.
A) 60°
B) 90°
C) 120°
D) 30°

Answer 1

Hint: The angle at which the two plane mirrors are placed decides the number of images one can obtain of a single object. As the angle between the two mirrors decreases, the number of images formed increases.

Formula Used: The number of images formed of a single object when two plane mirrors are placed at an angle $\theta $ is given by, $n = \dfrac{{360^\circ }}{\theta } - 1$ .

Complete step by step answer:
Step 1: List the data given in the question.
It is given that two plane mirrors placed at some angle produce three images of the single object.
Let $\theta $ be the angle between those two plane mirrors and let $n = 3$ be the number of images formed by the two mirrors.
Step 2: Obtain an expression for the angle between the two mirrors.
The number of images formed of a single object when two plane mirrors are placed at an angle $\theta $ is given by, $n = \dfrac{{360^\circ }}{\theta } - 1$ .
We rearrange the above relation to get, $\theta = \dfrac{{360^\circ }}{{n + 1}}$ ------- (1)
Step 3: Find the angle at which the two mirrors are placed using equation (1).
We have the number of images formed as $n = 3$ .
Equation (1) gives us, $\theta = \dfrac{{360^\circ }}{{n + 1}}$
Substituting the value for $n = 3$ in equation (1) we get, $\theta = \dfrac{{360^\circ }}{{3 + 1}} = 90^\circ $
$\therefore$ The two mirrors are placed at an angle $\theta = 90^\circ $ to obtain three images of a single object.
$\therefore$ (b) is the correct option.

Note: One mirror will produce one image. Two individual mirrors will produce two individual images. But when they are kept such that they are perpendicular to each other three images will be formed. If the two mirrors are facing each other then infinitely many images can be formed.