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.
$\therefore v_{m}=\frac{3 \times 10^{8}}{2}$
$=1.5 \times 10^{8}\, m / s$