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. $45^{\circ }$
• B. $75^{\circ }$
• C. $30^{\circ }$
• D. $60^{\circ }$

Answer 1

Answer: (C)

Angle between incident ray and reflected ray
$\cos \delta =\frac{(\hat{i}+\sqrt{3}\hat{j})\cdot (\hat{i}-3\hat{j})}{2\cdot 2}$

$\cos \delta =-\frac{1}{2}$
$\Rightarrow \delta =120^{\circ }$
$180-\angle i=120$
$\Rightarrow \angle i=30^{\circ }$