Question

A ray of light is incident on a glass plate making an angle of ${60}^{\circ }$ with the normal to the surface at the point of projection. If the reflected ray and refracted rays are perpendicular to each other, the refractive index of glass is :

• A. $\sqrt{3}$
• B. $\sqrt{\frac{3}{2}}$
• C. $\frac{3}{2}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\sqrt{3}$

At the interface of two medium, the direction $N{N}^{\prime }$ represents the normal direction.
From law's of reflection at the interface of two medium,
$\Rightarrow \angle i=\angle r={60}^{\circ }$
from Snell's law
$\frac{\sin i}{\sin r^{\prime }}={\mu }_g$ ......(1)



Given: Reflected ray and refracted ray are perpendicular
$\Rightarrow \angle r+{90}^{\circ }+\angle r^{\prime }={180}^{\circ }$
$\Rightarrow {60}^{\circ }+{90}^{\circ }+\angle r^{\prime }={180}^{\circ }$
$\therefore \angle r^{\prime }={180}^{\circ }-{150}^{\circ }={30}^{\circ }$
from Eq. (1)
$\Rightarrow \frac{\sin {60}^{\circ }}{\sin {30}^{\circ }}={\mu }_g$
$\therefore {\mu }_g=\frac{\sqrt{3}}{2}\times \frac{2}{1}=\sqrt{3}$
Hence, option $\left(a\right)$ is the correct answer.

Why this question? The intent is to make you think beyond the constraints of refraction while dealing with incidence of light ray at the boundary separating two medium. Tips: Apply laws of reflection as well as Snell's law at the interface in these type of questions.