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}$