the reflected ray is completely polarized for a certain angle of incidence in a transparent medium. If the angle of refraction is 30degree the the refractive index of the medium is

The reflected ray is completely polarised. This means that the incident ray is incident at the Brewster’s angle for the given pair of media. Hence, the reflected and refracted ray are at right angles to each other. Now the angle of incidence is equal to the angle of refraction. Hence, it follows that the angle of incidence and angle of refraction are complementary to each other. This gives the angle of incidence as 60^o.

 

Now tan theta = n/1             where theta is the angle of incidence and n is the refractive index of the second medium                                                    (assuming first medium to be air)

                       => n = tan(60^o)

                               = sqrt (3)

 

Hope it helps! All the best!