Question

Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror $\left(M_1\right)$ and parallel to the second mirror $\left(M_2\right)$ is finally reflected from second mirror $M_2$ parallel to the first mirror $\left(M_1\right)$. The angle between the two mirrors will be

• A. ${90}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is C ${60}^{\circ }$


Let $\theta$ be the angle between the mirrors.

Here, Ray $PQ||$ mirror $M_1$ and $RS||$ mirror $M_2$

$\therefore M_{1}RS=\angle ORQ=\angle M_{1}O{M}_2=\theta$

Similarly, $\angle M_{2}QP=\angle OQR=\angle M_{2}O{M}_1=\theta$

$\therefore \text{In}\Delta ORQ,\Rightarrow 3\theta ={180}^{\circ }\Rightarrow \theta =\frac{{180}^{\circ }}{3}={60}^{\circ }$

Hence, option $\left(B\right)$ is correct.