Question

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

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

Answer 1

The correct option is D $\sqrt{2}$

$\angle \text{i}={45}^{\circ }$
$\angle \text{r}={30}^{\circ }$
$\text{n}=\frac{\text{sin i}}{\text{sin r}}=\frac{\text{sin}{45}^{\circ }}{\text{sin}{30}^{\circ }}=\frac{\left(\frac{1}{\sqrt{2}}\right)}{\left(\frac{1}{2}\right)}=\sqrt{2}$
The refractive index of the medium is $\sqrt{2}$ or $1.414$.