Question

A mirror is placed at an angle of ${30}^o$ with respect to y-axis(see figure). A light rat 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)

$\sqrt{3}\hat{i}-\hat{j}$

As shown in the figure ray will make ${30}^o$ with x-axis.

$\therefore \theta =-30$

Slope of ray = $tan\theta$

=$tan(-{30}^o)$

=$-\frac{1}{\sqrt{3}}$

$\therefore$ y-coordinate is -1 because ray goes to negative y direction.

and x-coordinate is $\sqrt{3}$.

$\therefore$ vector is ,$\sqrt{3}\overline{i}-\overline{j}$