Q.12. When the angle of incidence on a material is 60$°$, the reflected light is completely polarized. The velocity of the refracted ray inside the material is (in $m{s}^{-1}$):
(A) 3$\times {10}^8$
(B) $\left(\frac{3}{\sqrt{2}}\right)$ $\times {10}^8$
(C) $\sqrt{3}$ $\times {10}^8$
(D) 0.5$\times {10}^8$
 

Dear Student,
                       As we know the Brewster's law, 
                                                                           Refractive index, $\mu = \tan {\theta }_B$
                                                                          Here given, ${\theta }_B$ = 60^o
                                                                           So, we have, 
                                                                                               $$\begin{gathered} \mu = \tan {60}^o \\ =\sqrt{3} \end{gathered}$$
                   Now the velocity of ray inside the material, $$\begin{gathered} v = \frac{c}{\mu }=\frac{3\times {10}^8}{\sqrt{3}} \\ =\sqrt{3}\times {10}^8 m/s. \end{gathered}$$
    Hence the correct option is (C).

Regards