Question

In the figure shown, find the angle $\left(\theta \right)$ by which mirror should be rotated. So that the ray of light retraces its path after reflection from mirror $M$.

• A. $\theta =2^{\circ }$ anticlockwise
• B. $\theta =1^{\circ }$ clockwise
• C. $\theta ={3.5}^{\circ }$ clockwise
• D. $\theta =3^{\circ }$ anticlockwise

Answer 1

The correct option is B $\theta =1^{\circ }$ clockwise

The angle of the given prism is small $(i.e.A=2^{\circ })$

$\Rightarrow$ Deviation produced by prism is given by :
$\delta =(\mu -1)A$
$\Rightarrow \delta =(1.5-1)2^{\circ }=1^{\circ }$
Hence, the emergent ray is deviated by $1^{\circ }$ from the original path, as shown in figure.


From laws of reflection, at the plane mirror
$i=r=1^{\circ }$

From the diagram shown, it is clear that if the mirror is rotated by $1^{\circ }$ clockwise, then the emergent ray from the prism would strike the mirror normally and light will retrace its path.

Why this question? Bottom line: The initial direction of the incident ray is along the normal to plane mirror however due to deviation produced by the prism the light ray did not fall normally on the mirror.