Question

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

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

Answer 1

Answer: (A)

$30^{\circ}$

Answer 2

Let angle between the directions of incident ray and reflected ray be $\theta$
$\cos \theta=\frac{1}{2}(\hat{i}+\sqrt{3} \hat{j}) \cdot \frac{1}{2}(\hat{i}-\sqrt{3} \hat{j})$
$\cos \theta=-\frac{1}{2}$
$\theta=120^{\circ}$