Question

Calculate the refractive index of the medium Y, when a light ray enters from air at an angle $\angle i={45}^{\circ }$, and $\angle r={30}^{\circ }$?

• A. 0.7

Answer 1

The correct option is A 0.7
Given:
Angle of incidence, $\angle i={45}^{\circ }$
Angle of refraction, $\angle r={30}^{\circ }$
Incident medium is air.

Refractive index of air, $n_a\approx 1$

Let the refractive index of the medium Y be $n_Y$, then using Snell's law,
$\frac{n_a}{n_Y}=\frac{\sin r}{\sin i}$
$n_Y=1\times \frac{\sin {30}^{\circ }}{\sin {45}^{\circ }}$
$n_Y=\frac{1/2}{1/\sqrt{2}}$
$n_Y=\frac{1}{\sqrt{2}}=0.707\approx 0.7$