Question

Two mirrors are inclined at an angle $\theta$ as shown in the figure. A light ray is incident parallel to one of the mirrors. What should be the value of $\theta$ such that the light will retrace its path after the third reflection?

Answer 1

It is clear that for third reflection the ray must hit the mirror normally, i.e., the angle of reflection $=0^{\circ }$.

In $\Delta$ OBC, $\angle OBC={90}^{\circ }-\theta$
$\therefore \angle CBN=\theta$
Now, in $\Delta$ ABC, $\theta +\theta +\theta +{90}^{\circ }={180}^{\circ }$
$\Rightarrow \theta ={30}^{\circ }$.