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. $4/3$

Answer 1

The correct option is D $4/3$

A ray of light is going from air to glass angle of refraction inside the glass

$90°={\theta }_r+{\theta }_d$

Since ${\theta }_r={\theta }_d$

${\theta }_r=$ angle of refraction inside the glass

${\theta }_d=$ angle of deviation inside the glass

$\therefore 90°=2{\theta }_r{\theta }_r=45°\mu =\frac{\sin {\theta }_i}{\sin 45°}\mu =\frac{\sqrt{2}/3}{1/\sqrt{2}}=\frac{4}{3}({\theta }_i=60°)$

Using Brewster's law

$tan\left({\theta }_p\right)=\frac{n_2}{n_1}\mu =tanip$

$\mu =\frac{\sin ip}{\sin ir}$