Question

An object is kept between two plane mirrors inclined at an angle $120$ from each other; calculate the ratio of number of images which are formed if the object is not on the angle bisector to the number of images formed if object is on the bisector?

• A. $\frac{3}{3}$
• B. $\frac{3}{2}$
• C. $\frac{2}{2}$
• D. $\frac{2}{3}$

Answer 1

Answer: (B)

$\frac{3}{2}$

Given: An object is kept between two plane mirrors inclined at an angle 120 from each other

To find the ratio of number of images which are formed if the object is not on the bisector and on the bisector

Solution:

If there are two plane mirrors inclined to each other at an angle $\theta$, the number of images of a point object formed are determined as follows:

If $\left(\frac{{360}^{\circ }}{\theta }\right)$ is odd integer (say $m$) number of images formed

$n=m$, if the object is not on the bisector of mirrors

$n=(m–1)$, if the object is on the bisector of mirrors.

So, when $\theta ={120}^{\circ }$, we get

$m=\frac{360}{120}=3$

So,

$\frac{\text{number of images which are formed if the object is not on the bisector}}{\text{number of images which are formed if the object is on the bisector}}=\frac{3}{3-1}=\frac{3}{2}$