Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror $(M_1)$ and parallel to the second mirror $(M_2)$ is finally reflected from the second mirror $(M_2)$ and parallel to the first mirror $(M_1)$. The angle between the two mirrors will be:
Answer: (A) $60^\circ$
Let the mirrors meet at angle $\theta$. The incident ray is parallel to $M_2$, so it meets $M_1$ at angle $\theta$; after reflection it leaves $M_1$ also at angle $\theta$.
The final ray is parallel to $M_1$, so it leaves $M_2$ at angle $\theta$ to $M_2$, and therefore also arrives at $M_2$ at angle $\theta$.
The ray between the mirrors and the two mirrors form a triangle with all three angles equal to $\theta$:
$$3\theta = 180^\circ \;\Rightarrow\; \theta = 60^\circ$$
Solution by Sreeraj P, M.Sc Physics