Question

A ray of light is going from air to glass such that the reflected light is found to be completely plane polarized. Also, the angle of refraction inside the glass is found exactly equal to the angle of deviation suffered by the ray. The refractive index of the glass is

• A. $1.5$
• B. $\sqrt{2}$
• C. $\sqrt{3}$
• D. $\frac{4}{3}$

Answer 1

The correct option is C $\sqrt{3}$


Given: $\delta =r$

When unpolarized light is incident at the polarizing angle, the reflected and refracted light are perpendicular.

$\therefore i_p+r={90}^{\circ }$

$\Rightarrow i_P={90}^{\circ }-r...\left(1\right)$

Angle of deviation $\delta =i_p-r$

As, $\delta =r$

$\therefore r=i_p-r$

$\Rightarrow i_p=2r$

$\Rightarrow r=\frac{i_p}{2}...\left(2\right)$

From equation $\left(1\right)$

$i_p={90}^{\circ }-r$

$\Rightarrow i_p={90}^{\circ }-\frac{i_p}{2}$

$\Rightarrow i_p={60}^{\circ }$

From Brewster's law

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

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