Question

The reflected and refracted rays are observed to be perpendicular to each other, when ray of light is incident at an angle of ${60}^{\circ }$ on a transparent block. The refractive index of that block is:

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

Answer 1

Answer: (D)

$\sqrt{3}$

So, by Snell's Law
$\frac{{\mu }_1}{{\mu }_2}=\frac{\sin {\theta }_2}{\sin {\theta }_1}$
$=\frac{\sin {30}^{\circ }}{\sin {60}^{\circ }}$
$=\frac{1/2}{\sqrt{3}/2}$ $(\sin {60}^{\circ }=\sqrt{3}/2;\sin {30}^{\circ }=1/2)$
$=\frac{1}{\sqrt{3}}$
So, $\frac{{\mu }_2}{{\mu }_1}=\sqrt{3}$
or ${\mu }_2=\sqrt{3}\left({\mu }_1\right)$

$=\sqrt{3}\left(1\right)$ $(\because {\mu }_1=1)$
$=\sqrt{3}$