Question

If the critical angle for total internal reflection from medium to vacuum is $30{}^{\circ }$ , the velocity of light in medium is

• A. $3\times {10}^{8}m/s$
• B. $1.5\times {10}^{8}m/s$
• C. $6\times {10}^{8}m/s$
• D. $\sqrt{3}\times {10}^{8}m/s$

Answer 1

Answer: (B)

Refractive index medium $\mu =\frac{1}{\sin C}$
where $C$ is critical angle.
Given, $C=30^{\circ }$
$\therefore \mu =\frac{1}{\sin 30^{\circ }}=\frac{1}{1/2}=2$
From Snell's law
$\mu =\frac{v_0}{v_m}$
where $v_0$ is speed of light in vacuum and $v_m$ the velocity in medium.
$\therefore v_m=\frac{3\times 10^8}{2}$
$=1.5\times 10^{8}m/s$