Question

Onto 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 the glass 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, the angle of refraction, $r={180}^{\circ }-({60}^{\circ }+{90}^{\circ })={30}^{\circ }$

$\therefore$ refractive index of the glass, $\mu =\frac{\text{sin i}}{\text{sin r}}=\frac{\text{sin}{60}^{\circ }}{\text{sin}{30}^{\circ }}=\frac{\left(\frac{\sqrt{3}}{2}\right)}{\left(\frac{1}{2}\right)}=\sqrt{3}$