Question

When the angle of incidence on a material is ${60}^{\circ }$, the reflected light is completely polarized. The velocity of the refracted ray inside the material is $\left({\text{in ms}}^{-1}\right)$

• A. $0.5\times {10}^8$
  
• B. $3\times {10}^8$
• C. $\sqrt{3}\times {10}^8$
• D. $\left(\frac{3}{\sqrt{2}}\right)\times {10}^8$

Answer 1

The correct option is C $\sqrt{3}\times {10}^8$

The reflected ray will be completely polarized when the angle of incidence is equal to polarizing angle.

By Brewster's law,

$\tan i_p=\mu$

Where, $\mu \to$ Refractive index of the material

Here, $i_p={60}^{\circ }$

$\Rightarrow \mu =\tan {60}^{\circ }=\sqrt{3}$

We know that,

$\mu =\frac{c}{v}$

Where, $v$ is the velocity of light in the material.

$\Rightarrow \sqrt{3}=\frac{3\times {10}^8}{v}$

$\Rightarrow v=\frac{3\times {10}^8}{\sqrt{3}}=\sqrt{3}\times {10}^8{\text{ms}}^{-1}$

Hence, option $\left(C\right)$ is correct.

Why this question? Key concept: When the angle of incidence is equal to the angle of polarization, $i_p$, $\tan i_p=\mu$