Question

Two plane mirrors are inclined at angle $\theta$ if any ray incident on one mirror becomes anti-parallel after reflection from the other mirror then the angle $\theta$ can be

• A. less than ${90}^{\circ }$
• B. ${90}^{\circ }$
• C. more than ${90}^{\circ }$
• D. Cannot be determined

Answer 1

The correct option is B

${90}^{\circ }$

Step 1: Anti-parallel rays:

1. Anti-parallel rays are the rays, which are parallel in nature, but opposite in direction.
2. Considering anti-parallel rays, the mirrors can be drawn as follows:

Step 2: Calculation of total deviation angle

The equation for the total deviation angle can be written as follows:

$\delta ={360}^{\circ }-2\theta$

Here,

$\delta$ is the total deviation angle.

$\theta$ is the angle between the mirrors.

Since the rays are anti-parallel, the total deviation is ${180}^{\circ }$.

$$\begin{gathered} {180}^{\circ }={360}^{\circ }-2\theta \\ 2\theta ={180}^{\circ } \\ \theta ={90}^{\circ } \end{gathered}$$

Hence, the required angle between the mirrors is ${90}^{\circ }$.

Therefore, option (B) is correct.