Question

If a ray travelling in the direction $\frac{1}{2}(\hat{i}+\sqrt{3}\hat{j})$ is incident on a plane mirror. After reflection, the ray travels along the direction $\frac{1}{2}(\hat{i}-\sqrt{3}\hat{j})$.
The angle of incidence is :

• A. ${45}^o$
• B. ${75}^o$
• C. ${30}^o$
• D. ${60}^o$

Answer 1

Answer: (C)

${30}^o$

Angle between incident ray and reflected ray

$\cos \delta =\frac{(\hat{i}+\sqrt{3}\hat{j})\cdot (\hat{i}-3\hat{j})}{2\cdot 2}$

$\cos \delta =-\frac{1}{2}\Rightarrow \delta ={120}^o$

We will use dot product of two vector to find the angle :

$ABcos\theta =\overrightarrow{A}.\overrightarrow{B}$

From here we will get $cos\delta =-\frac{1}{2}$

$⟹\delta ={120}^o$

From figure also , ${180}^o-\angle 2i={120}^o$

$\therefore \angle i={30}^o$