Question

Two mirrors are kept at an angle ${60}^{\circ }$ between them as shown in the fig. A ray of light strikes the first mirror and after reflection strikes the second mirror. If the final reflected ray goes parallel to the first mirror, calculate the angle of incidence.

• A. ${10}^{\circ }$
• B. ${20}^{\circ }$
• C. ${30}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is C

${30}^{\circ }$

Lets draw the ray diagram as mentioned in the problem.

$\angle 1={90}^{\circ }-\theta$ (Angle of incidence = angle of reflection) ...1)
$\angle 1=\angle 3+\angle 4$ (Alternate opposite angles) ...2)
$\angle 3=\angle 4$ (Angle of incidence = angle of reflection) ...3)
From above three we get,
$\angle 3={45}^{\circ }-\frac{\theta }{2}.$
$\angle 3+\angle 2={90}^{\circ }.$
(as BD is the normal)
Hence
$\angle 2={45}^{\circ }+\frac{\theta }{2}$
Now, in triangle, ABO
$\angle 1+\angle 2+{60}^{\circ }={180}^{\circ }$
Substituting $\angle 1\&\angle 2$, we get
${90}^{\circ }-\theta +{45}^{\circ }+\frac{\theta }{2}={120}^{\circ }$
From above equation
$\frac{\theta }{2}={15}^{\circ }$
Or,
$\theta ={30}^{\circ }$