Question: 27. An unpolarized light beam travelling in air is incident on a medium of refractive index 1.73 at Brewster’s angle. Then-
(1) reflected light is completely polarized and the angle of reflection is close to 60^{\circ}
(2) reflected light is partially polarized and the angle of reflection is close to 30^{\circ}.
(3) both reflected and transmitted light are perfectly polarized with angles of reflection
and refraction close to 60^{\circ} and 30^{\circ}, respectively.
(4) transmitted light is completely polarized with angle of refraction close to 30^{\circ}
Answer: Option (1)
Explanation:
Brewster’s angle \theta_B is given by the relation
\tan\theta_B=\dfrac{n_2}{n_1},
where n_1 and n_2
are refractive indices of the first and second medium.
Here air has n_1=1 and the medium has n_2=1.73.
Calculate \theta_B:
\tan\theta_B=\dfrac{1.73}{1}=1.73\Rightarrow \theta_B=\tan^{-1}(1.73)\approx 60^{\circ}.At Brewster’s angle the reflected light is completely (linearly) polarized with its electric vector perpendicular to the plane of incidence.
Also the angle of reflection equals the angle of incidence,
so the reflected ray makes an angle close to 60^{\circ} with the normal.
For the refracted (transmitted) ray find the refraction angle r using Snell’s law:
n_1\sin\theta_B=n_2\sin r \Rightarrow \sin r=\dfrac{n_1}{n_2}\sin\theta_B=\dfrac{1}{1.73}\sin 60^{\circ}=\dfrac{0.8660}{1.73}\approx 0.50 \Rightarrow r\approx 30^{\circ}.However, the transmitted light is not perfectly polarized;
only the reflected component is completely polarized at Brewster’s angle.
Therefore statement (1) is the correct choice:
reflected light is completely polarized and the angle of reflection is close to 60^{\circ}.