Question 12

For the reflected ray $CD$ to be completely polarized, the light must be incident at the Brewster's angle $\theta_B$ at the interface between the water ($n_w$) and the medium ($n_p$).

According to Brewster's law:

$\tan \theta_B = \frac{n_p}{n_w} = \frac{4/\sqrt{3}}{4/3} = \sqrt{3}$

$\Rightarrow \theta_B = 60^\circ$

Since the glass plate and water layers are parallel, we apply Snell's law across the layers:

$n_w \sin i = n_g \sin r = n_w \sin \theta_B$ $\Rightarrow \sin i = \sin \theta_B$ $\Rightarrow i = 60^\circ$