Question

Two plane mirrors subtend an angle$\theta$. Light incident on one mirror after reflection from the other mirror returns parallel to the original direction. The angle$\theta$must be

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${90}^o$

Answer 1

The correct option is D

${90}^o$

1. Assume that the two plane mirrors subtend the angle $\theta$.
2. We know that the Incident angle and Reflection angles are equal for plane mirror reflection. Therefore, assume that $\alpha$is the incident angle and therefore reflection angle of the incident ray on the first mirror as shown in the figure.
3. It is given that the reflected ray from the second mirror is parallel to the original incident ray on the first ray. Using simple geometry we can see that $\angle PQR=180-2\alpha$.
4. Therefore, as shown in the figure, we can use the law of complementary angles to conclude that $\angle QRS=2\alpha$.
5. Therefore, we see that $180-\alpha -\theta +180-\alpha -\theta +2\alpha =180$

Or, $360-2\theta =180$

Or, $2\theta =180$

Or, $\theta =90$

Therefore, correct option is (d) ${90}^{\circ }$