Question

A ray of light is incident on a plane mirror along a line represented by $\hat{i}+\hat{j}+\hat{k}$. Normal to the mirror of the incidence point is along the vector $\hat{i}+\hat{j}$ unit vector along the reflected ray is.

• A. $2\hat{i}+4\hat{j}+2\hat{k}$
• B. $\hat{i}-\hat{j}-\hat{k}$
• C. $-\frac{1}{\sqrt{3}}\left(\hat{i}+\hat{j}+\hat{k}\right)$
• D. $-\hat{i}-\hat{j}-\hat{k}$

Answer 1

The correct option is C $-\frac{1}{\sqrt{3}}\left(\hat{i}+\hat{j}+\hat{k}\right)$

$\begin{array}{c}\widehat{e_r}=\frac{\hat{i}+\hat{j}-\hat{k}}{\sqrt{3}}\\ \hat{n}=\frac{\hat{i}+\hat{j}}{\sqrt{2}}\\ \widehat{e_r}={\hat{e}}_i-2\left({\hat{e}}_i-\right)\hat{n}\\ =-\frac{1}{\sqrt{3}}\left(\hat{i}+\hat{j}+\hat{k}\right)\end{array}$