Question

Find the number of images formed by the system of plane mirrors arranged as shown in the figure, if the object is placed at ${}^{\prime }{\text{O}}^{\prime }$.

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is D $5$


The mirrors are at $\theta ={70}^{\circ }$ to each other.

Number of images formed $=\frac{360}{\theta }=\frac{360}{70}=5.14$ (not an integer)

From the figure given in the question, by symmetry, the first image formed by the mirror -II is also at ${30}^{\circ }\circlearrowright$ with respect to mirror-II.

Similarly, first image formed by the mirror-I is at ${40}^{\circ }\circlearrowleft$ with respect to mirror-I.

First image formed by mirror-I acts as an object for mirror -II whose image will be formed at ${110}^{\circ }\circlearrowright$ with respect to mirror-II.

First image formed by mirror-II acts as an object for mirror -I whose image will be formed at ${100}^{\circ }\circlearrowleft$ with respect to mirror-I.

Second image formed by mirror-I acts as an object for mirror -II whose image will be formed at ${170}^{\circ }$ with respect to mirror-II.

Second image formed by mirror-II acts as an object for mirror -I whose image will be formed at ${180}^{\circ }$ with respect to mirror-I i.e image is not formed.

$\therefore$ Number of images formed by the given arrangement of mirrors is $5$.