Question

On a glass plate a light wave is incident at an angle of ${60}^{\circ }$. If the reflected and the refracted waves are mutually perpendicular, the refractive index of material is

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

Answer 1

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

from figure

Angle of refraction $=\angle r$
Angle of incidence is equal to angle of reflection [law of reflection]
$\therefore$ Angle of reflection $={60}^{\circ }$
Given that reflected and refracted ray are perpendicular.
From figure
${60}^{\circ }+{90}^{\circ }+\angle r={180}^{\circ }$ [angle sum property]
$\angle r={30}^{\circ }$
$\angle i={60}^{\circ },\angle r={30}^{\circ }$
so $\mu =\frac{sin60}{sin30}=\sqrt{3}$