Question

A light source lies at the angle bisector of two plane mirrors inclined at an angle of $\theta$. The limitation for the value of $\theta$ so that the light reflected from one mirror does not reach the other mirror will be

• A. $\theta \le {120}^{\circ }$
• B. $\theta \le {90}^{\circ }$
• C. $\theta \ge {120}^{\circ }$
• D. $\theta \ge {60}^{\circ }$

Answer 1

The correct option is C $\theta \ge {120}^{\circ }$

For the symmetric placement (object lies at angle bisector), the number of images formed will be
$N=n-1=\frac{{360}^{\circ }}{\theta }-1$, irrespective of $\frac{{360}^{\circ }}{\theta }$ being even or odd.
For no successive reflection to occur, number of image formed will be 2 (1 each from individual mirror)
$N\le 2$
$\Rightarrow n-1\le 2$
$\Rightarrow n\le 3$
$\Rightarrow \frac{{360}^{\circ }}{\theta }\le 3$
$\Rightarrow \theta \ge {120}^{\circ }$