Question

A ray of light falls on a plane mirror. When the mirror is turned clockwise about an axis along the plane of the mirror by ${20}^{\circ }$, the incident ray gets deflected by ${45}^{\circ }$. The original incidence angle is

• A. ${80.5}^{\circ }$
• B. ${65.5}^{\circ }$
• C. ${45.5}^{\circ }$
• D. ${87.5}^{\circ }$

Answer 1

The correct option is D ${87.5}^{\circ }$

Given, the angle between the incident ray and the reflected ray after the mirror has been rotated is ${45}^{\circ }$.
Let the new angle of incidence is $\theta$.
So, ${45}^{\circ }={180}^{\circ }-2\theta$
$\Rightarrow \theta ={67.5}^{\circ }$


From figure, the original incidence angle,
$i={20}^{\circ }+\theta ={20}^{\circ }+{67.5}^{\circ }={87.5}^{\circ }$