Question

A mirror is placed at an angle of $30°$ with respect to Y-axis (see figure). A light ray travelling in the negative y-direction strikes the mirror. The direction of the reflected ray is given by the vector

• A. $\hat{i}$
• B. $\hat{i}-\sqrt{3}\hat{j}$
• C. $\sqrt{3}\hat{i}-\hat{j}$
• D. $\hat{i}-2\hat{j}$

Answer 1

Answer: (C)

Following laws of reflection, reflected ray makes an angle of $30^{\circ}$ with mirror as shown below.

So if a vector $x\hat{i}+y\hat{j}$ is along the reflected ray, then tan $(-30^{\circ}) =\frac{y}{x}or \frac{y}{x}=-\frac{1}{\sqrt{3}}$