Question

If the critical angle for the total internal reflection from a medium to vacuum is $30°$. The velocity of light in the medium is

• A. $1.5\times {10}^{8}m/s$
• B. $2\times {10}^{8}m/s$
• C. $3\times {10}^{8}m/s$
• D. $0.75\times {10}^{8}m/s$

Answer 1

The correct option is A $1.5\times {10}^{8}m/s$

We know that at critical angle $i_c$,
$n_{12}=\frac{1}{\sin i_c}$
where $n_{12}$ is the refractive index of medium 1 with repect to medium 2.
$n_{12}=\frac{1}{\sin 30°}{n}_{12}=2$
Speed of the light in the medium is given by
$v_m=\frac{v_v}{2}$
where, $v_v$ is speed of light in vacuum
⇒ $v_m=\frac{3\times {10}^8}{2}=1.5\times {10}^{8}m/s$