Question

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

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${75}^o$

Answer 1

Answer: (A)

${30}^o$

After reflection, the only component of the direction of propagation of incident light that is perpendicular to the plane mirror changes its sign
Here, as the $y$ component changes after reflection, we can assume that the direction of normal of the plane mirror is along with $\hat{j}$. Therefore angle of incidence is angle between the unit vectors $\frac{1}{2}(\hat{i}+\sqrt{3}\hat{j})$ and $\hat{j}$

$\Rightarrow cos\left(i\right)=\frac{1}{2}(\hat{i}+\sqrt{3}\hat{j}).\hat{j}$
$\Rightarrow i=co{s}^{-1}\frac{\sqrt{3}}{2}={30}^{\circ }$