Question

Two plane mirror A and B are inclined at angle $\theta (<{90}^o)$ to each other. A light ray parallel to mirror B is incident on mirror A and it becomes parallel to mirror A after reflection from mirror B. Find the value of angle $\theta$.

Answer 1

Let $\theta$ be the angle between mirrors $O{M}_1$ and $O{M}_2$

The incident light is reflected along BC.

Angle of reflection is $\alpha$.

From the figure we have,

$\angle M_{1}BA=\angle OBC=\angle M_{1}O{M}_2=\theta$

Similiarly, $\angle M_{2}CD=\angle BCO=\angle M_{2}O{M}_1=\theta$

Now in triangle OBC, $3\theta ={180}^{\circ }$

$\theta ={60}^{\circ }$