Question

A light incident at an interface at an angle ${60}^o$ is refracted into another medium at an angle ${30}^o$. If its speed in the first medium is C, then its speed in the second medium is

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

Answer 1

The correct option is D $\frac{C}{\sqrt{3}}$

A light incident at an interface at an angle ${60}^{\circ }(=i)$ is refracted into another medium at an angle ${30}^{\circ }(=r)$.

Given, its speed in the first medium i.e., in the air is $C$.

Let, speed of that light in the second medium is $v$.

We know, speed of light in second medium can be calculated from the refractive index $n$ of the second medium using the following equation:

$n=\frac{C}{v}$

Again, using Snell's law, $n=\frac{sini}{sinr}$

So, $\frac{C}{v}=\frac{sin{60}^{\circ }}{sin{30}^{\circ }}=\frac{\sqrt{3}/2}{1/2}=\sqrt{3}$

Therefore, $v=\frac{C}{\sqrt{3}}$

So, the correct option is - (D) $v=\frac{C}{\sqrt{3}}$.