Question

A ray of light traveling in the air is incident on the plane of a transparent medium. The angle of the incident is 45${}^o$ and that of refraction is 30${}^o$. Find the refractive index of the medium.

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

Answer 1

Answer: (D)

$\sqrt{2}$

Snell's Law of refraction gives the relation between the incident and refracted light at the interface of two media, which is given by $\frac{{\mu }_2}{{\mu }_1}=\frac{\sin i}{\sin r}$

The initial medium is air. Thus ${\mu }_1=1$

Given incidence angle $i={45}^o$ and refraction angle is ${30}^o$

By Snell's law, ${\mu }_2={\mu }_1\times \frac{\sin i}{\sin r}=1\times \frac{\sin {45}^o}{\sin {30}^o}=\frac{1/\sqrt{2}}{1/2}=\sqrt{2}$