Question

Two plane mirrors $M_1$ and $M_2$ are kept at angle $\theta^{\circ}$ with respect to each other. A light ray incident on $M_1$ parallel to $M_2$. If light ray retraces its path after third reflection, find value of $\frac{\theta}{5}$.

• A. 12
• B. 10
• C. 15
• D. 6

Answer 1

Answer: (A)

12

Answer 2

For a light ray to retrace its path after $n$ reflections between two mirrors inclined at an angle $\theta$, the condition is $\theta = \frac{180^{\circ}}{n}$ or $\theta = \frac{360^{\circ}}{n}$.

In this problem, the ray retraces its path after the third reflection. This means $n=3$. The condition for retracing the path implies that the ray is incident normally on the mirror from which it is reflected for the last time (the third reflection).

Using the formula $\theta = \frac{180^{\circ}}{n}$: $\theta = \frac{180^{\circ}}{3} = 60^{\circ}$.

The question asks for the value of $\frac{\theta}{5}$. $\frac{\theta}{5} = \frac{60^{\circ}}{5} = 12^{\circ}$.