Question

In figure, a ray of light undergoes refraction from medium $A$ to medium $B$. If the speed of light in medium $A$ is $v$, then the speed of light in medium $B$ will be

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

Answer 1

The correct option is A $\sqrt{3}v$

Here
Incident angle $\angle i={90}^{\circ }-{60}^{\circ }={30}^{\circ }$
Refractive angle $\angle r={90}^{\circ }-{30}^{\circ }={60}^{\circ }$
By Snells's law
$n_1\sin i=n_2\sin r$
$\frac{n_1}{n_2}=\frac{\sin r}{\sin i}$
$=\frac{\sin {60}^{\circ }}{\sin {30}^{\circ }}$
$=\frac{\sqrt{3}\times 2}{2\times 1}=\sqrt{3}$
$\frac{n_1}{n_2}=\frac{v_2}{v_1}=\sqrt{3}$
$v_2=\sqrt{3}{v}_1=\sqrt{3}v$
Hence, option $\left(1\right)$ is correct.