An unpolarised light is incident at an interface of two dielectric media having refractive indices of $2$ (incident medium) and $2\sqrt{3}$ (refracted medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is ___.

Question

A beam of unpolarised light of intensity $ I_0 $ is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of 45° relative to that of A. The intensity of emergent light is:

Answer 1

To determine the angle of incidence such that the reflected and refracted rays are perpendicular, we can utilize the concept of Brewster's angle. When the reflected and refracted rays are perpendicular, the angle of incidence is known as Brewster's angle.

Brewster's angle, denoted as $ \theta_B $, can be calculated using the formula:

\[\tan \theta_B = \frac{n_2}{n_1}\]

Where:

$ n_1 $ is the refractive index of the first medium (incident medium).
$ n_2 $ is the refractive index of the second medium (refracted medium).

In this problem:

$ n_1 = 2 $
$ n_2 = 2\sqrt{3} $

Substituting the given values into the Brewster's angle formula:

\[\tan \theta_B = \frac{2\sqrt{3}}{2} = \sqrt{3}\]

The angle whose tangent is $ \sqrt{3} $ is $ 60^\circ $, as:

\[\tan 60^\circ = \sqrt{3}\]

Therefore, the angle of incidence $ \theta_B $ is $ 60^\circ $.

Thus, the correct answer is: $ 60^\circ $

Answer 2