Question

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

• A. $30$
• B. $45$
• C. $60$
• D. $75$

Answer 1

The correct option is A $30$

In the first diagram,

$\overrightarrow{I}=\frac{1}{2}(i+\sqrt{3}j)\overrightarrow{I}=\cos 60°i+\sin 60°j$

In the second diagram,

$\overrightarrow{R}=\frac{1}{2}(i-\sqrt{3}j)\overrightarrow{R}=\cos 60°i-\sin 60°j\therefore \theta =60°$

If $\theta =60°$

then $\alpha =30°$

$\therefore$Angle of incidence=Angle of refelction=$\alpha$=$30°$