Question

A ray of light is incident on the surface of separation of a medium at an angle ${45}^{\circ }$ and is refracted in the medium at an angle of ${30}^{\circ }$. What will be the speed of light in the medium?

• A. $1.96\times {10}^{8}m/s$
• B. $2.12\times {10}^{8}m/s$
• C. $3.18\times {10}^{8}m/s$
• D. $3.33\times {10}^{8}m/s$

Answer 1

The correct option is B $2.12\times {10}^{8}m/s$

Refractive index, $n=\frac{\sin i}{\sin r}=\frac{c}{v}$
Hence, speed of sound in the medium $v=\frac{c\sin r}{\sin i}=\frac{3\times {10}^8\times \sin {30}^{\circ }}{\sin {45}^{\circ }}$

$v=\frac{3\times {10}^8}{\sqrt{2}}m/s$

$v=2.12\times {10}^{8}m/s$