Question

For the given situation shown below,find the angle from horizontal the mirror must be rotated in order to get a vertical reflected ray

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${15}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${30}^{\circ }$

Let, $\text{N}$ denotes the initial normal to the mirror and $\text{N'}$ is the normal to the mirror when it is rotated by $\theta$ in anticlockwise as shown in figure below.


From the figure, the angle between old normal $N$ and new normal $N^{\prime }$ is $\theta$.

As per question, we want vertical reflected ray.

Angle of incidence with the new normal is ${60}^{\circ }-\theta$

$\therefore$ Angle of incidence is ${60}^{\circ }-\theta$
and angle of reflection is $\theta$.

Applying law of reflection for vertical reflected ray,

$\text{Angle of reflection=Angle of incidence}$

$\Rightarrow \theta ={60}^{\circ }-\theta$

$\Rightarrow 2\theta ={60}^{\circ }$

$\Rightarrow \theta ={30}^{\circ }$

Hence, option $\left(b\right)$ is the correct answer.

Why this question: To under the effect of rotation of mirror on the angle of incidence and angle of reflection.