Question

A wavefront expressed by $x+y+z=4$ is incident on a plane mirror which is lying parallel to $xy-$ plane. Which of the following unit vectors correctly represent the direction of reflected ray ?

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

Answer 1

The correct option is B $\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})$

A Light ray is normal to the wavefront. Incident ray is parallel to $\overrightarrow{a}=\hat{i}+\hat{j}-\hat{k}$

The normal to the surface is parallel to $z-$ axis. The component of $\overrightarrow{a}$ parallel to $xy$ plane doesn not change during reflection and the $z-$ component gets reversed.

Therefore, a vector in the direction of reflected ray is $\overrightarrow{b}=\hat{i}+\hat{j}+\hat{k}$

Unit vector along $\overrightarrow{b}$ is $\hat{b}=\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})$

Hence, option (b) is the correct answer.