A light ray is incident, at an incident angle $\theta_1$, on the system of two plane mirrors $M_1$ and $M_2$ having an inclination angle $75^\circ$ between them (as shown in figure). After reflecting from mirror $M_1$ it gets reflected back by the mirror $M_2$ with an angle of reflection $30^\circ$. The total deviation of the ray will be ______ degree.
Numerical value type. Enter your answer.
Answer: 210
With angle of reflection $30^\circ$ at $M_2$, the ray meets $M_2$ at $60^\circ$ to its surface. In the triangle formed with the mirrors, the ray meets $M_1$ at $180^\circ - 75^\circ - 60^\circ = 45^\circ$ to its surface, so $\theta_1 = 45^\circ$.
Deviation at $M_1$: $180^\circ - 2(45^\circ) = 90^\circ$. Deviation at $M_2$: $180^\circ - 2(30^\circ) = 120^\circ$.
Total deviation $= 90^\circ + 120^\circ = 210^\circ$ (which also equals $360^\circ - 2\times75^\circ$).
Solution by Sreeraj P, M.Sc Physics