Question

A ray of light makes an angle of ${10}^{\circ }$ with the horizontal and strikes a plane mirror which is inclined at an angle $\alpha$ to the horizontal. The angle $\alpha$ for which the reflected ray becomes vertical is :

• A. ${40}^{\circ }$
• B. ${30}^{\circ }$
• C. ${60}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is D ${50}^{\circ }$

Given that:

$\angle IOH={10}^o$

The mirror is inclined at an angle $\alpha$

From the figure above;

Incident angle $i=\angle ION=(90-\alpha )+10$

Therefore,

Reflected angle, $r=\angle RON=(90-\alpha +10)$

Thus,

$\angle HOR=i+r-10$

If the reflected ray become vertical,

$\angle HOR=90=i+r-10$

$90=100-\alpha +100-\alpha -10$

$90=190-2\alpha$

$\alpha ={50}^o$

Therefore, for the reflected ray to be vertical, the mirror should be inclined at an angle of ${50}^o$.