Question

Two plane mirrors are arranged at right angles to each other. A ray of light is incident on the horizontal mirror at an angle $\theta$. For what value of $\theta$, the ray emerges parallel to the incoming ray after reflection from the vertical mirror?

• A. ${60}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. All of the above

Answer 1

The correct option is D All of the above


Let $N_1$ and $N_2$ be the normal at both mirrors.
At mirror $1$,
$\angle i=\theta =\angle r$
At mirror $2$,
$\angle i=90-\theta$
Hence, the reflected ray makes an angle $(90-\theta )$ from normal $N_2$ which is horizontal.
Thus, incident and reflected rays become parallel as both make $(90-\theta )$ from horizontal.
$\therefore$ It holds true for all values of $\theta$.
For two mirrors inclined at ${90}^{\circ }$, the final reflected ray always emerges parallel to the incident ray.
Hence, option $\left(d\right)$ is the correct answer.