Question

If the critical angle for total internal reflection from a medium to vacuum is ${30}^o$. Then velocity of light in the medium is:

• A. $3\times {10}^{8}m/s$
• B. $4.5\times {10}^{8}m/s$
• C. $1.5\times {10}^{8}m/s$
• D. $2.5\times {10}^{8}m/s$

Answer 1

Answer: (C)

$1.5\times {10}^{8}m/s$

Critical angle for total internal reflection ${\theta }_c={30}^o$

As we know, refractive index of air medium $n_{air}=1$

Refractive index of the medium $n=\frac{1}{\sin {\theta }_c}$

$\therefore$ $n=\frac{1}{\sin {30}^o}=\frac{1}{0.5}$

$⟹$ $n=2$

Velocity of light in medium $v=\frac{c}{n}$

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