Question

Two mirrors are held normal to each other. A ray of light is incident on one mirror at an angle ${30}^{\circ }$ as shown in figure.

What is the angle of reflection from mirror $M_2$?

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$


In the figure
$AR$ is the incident ray on Mirror $M_1$ and $CS$ is the reflected ray from Mirror $M_2$
$AM$ is Normal on Mirror $M_1$
Angle of incidence on Mirror $M_1\angle RAM={30}^{\circ }$
Using Law of reflection
Angle of incidence $\angle RAM=$Angle of reflection $\angle MAC$
So angle of reflection $\angle MAC={30}^{\circ }$ after first reflection
Reflected ray from $M_1$ acts as incident ray on $M_2$
Angle between the mirrors is ${90}^{\circ }$
Normal $AM$ is parallel to mirror $M_2$
So $\angle ACB=\angle MAC={30}^{\circ }$ (Alternating angles)
Angle of incident on mirror $M_2=\angle ACN={90}^{\circ }-{30}^{\circ }={60}^{\circ }$
Using law of reflection
Angle of incidence $\angle ACN=$ Angle of reflection $\angle NCS$
So angle of reflection $\angle NCS={60}^{\circ }$ from the second mirror $M_2$