Question

A ray of light is approaching a set of three mirrors as shown in the diagram. The light ray is approaching the first mirror at an angle of ${45}^{\circ }$ with the mirror surface. How many times will the ray reflect before it exits the system?

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$


At mirror $1$, angle of incidence
$\angle i={45}^{\circ }$
$\Rightarrow \angle r=\angle i={45}^{\circ }$
Hence $\angle r+\angle i={90}^{\circ }$ i.e. ray will go horizontally at mirror $2$.
Here $\angle r={90}^{\circ }-{45}^{\circ }={45}^{\circ }$
$\therefore \angle i=\angle r={45}^{\circ }$
$\Rightarrow \angle i+\angle r={90}^{\circ }$
Hence reflected ray goes past mirror, vertically.
$\therefore$ After $2$ reflection, ray exist the system.
Hence, option $\left(b\right)$ is the correct answer.