Question

In the figure shown, the incident ray is rotated by $2^{\circ }$ in clockwise sense, the mirror is rotated by $8^{\circ }$ in clockwise sense, then the angle by which reflected ray will be rotated is

• A. ${10}^{\circ }$ clockwise
• B. ${14}^{\circ }$ anticlockwise
• C. ${16}^{\circ }$ Clockwise
• D. ${14}^{\circ }$ clockwise

Answer 1

The correct option is D ${14}^{\circ }$ clockwise

Given,

Rotation of incident ray is $2^{\circ }\circlearrowright$

Rotation of mirror is $8^{\circ }\circlearrowright$

If the mirror is rotated by $\theta$ , reflected ray rotates by $2\theta$ in the same sense.

Due to rotation of mirror, reflected ray rotates by ${16}^{\circ }\circlearrowright$ .

If incident ray rotates by $\theta$ , reflected ray rotates by $\theta$ in the opposite sense.


Due to rotation of incident ray , reflected ray rotates by $2^{\circ }\circlearrowleft$.

Net rotation of reflected ray is given by

${16}^{\circ }\circlearrowright +2^{\circ }\circlearrowleft ={14}^{\circ }\circlearrowright$

Hence, option (d) is the correct answer.

$\begin{array}{c}\text{Why this Question}?\\ \text{This question provides student a conceptual clarity of rotation of mirror, incident \& reflected ray.}\\ \\ \text{Note-1 :- The angle turned by the reflected ray is twice the angle turned by the mirror.}\\ \text{Note-2 :- If mirror rotates clockwise, then reflected ray will rotate clockwise.}\\ \text{Note -3 :- If the mirror is kept fixed and the incident ray is rotated,then the reflected ray will}\\ \text{rotate in opposite sense by same angle.}\end{array}$