Analyzing Light Polarization at an Interface

This question examines the polarization of light after reflection from an interface between two different dielectric media. The key factors are the dielectric constants of the media, the magnetic permeability, and the angle of incidence.

Calculating Refractive Index Ratio

The refractive index ($n$) is related to the dielectric constant ($\epsilon$) and magnetic permeability ($\mu$) by the formula $n = \sqrt{\epsilon \mu}$.

Given that the magnetic permeability is identical for both media ($\mu_1 = \mu_2$), the ratio of the refractive indices depends solely on the ratio of the square roots of their dielectric constants.

Let $n_1$ and $n_2$ be the refractive indices of the first and second media, respectively.

We have $\epsilon_2 = 3\epsilon_1$. Therefore:

$ \frac{n_2}{n_1} = \sqrt{\frac{\epsilon_2 \mu_2}{\epsilon_1 \mu_1}} = \sqrt{\frac{3\epsilon_1 \mu_1}{\epsilon_1 \mu_1}} = \sqrt{3} $

Finding Brewster's Angle

Brewster's angle ($\theta_B$) is the angle of incidence where the reflected light is completely polarized in one direction.

For light traveling from medium 1 to medium 2, Brewster's angle is defined by:

$ \tan(\theta_B) = \frac{n_2}{n_1} $

Using the calculated ratio:

$ \tan(\theta_B) = \sqrt{3} $

Solving for $\theta_B$:

$ \theta_B = \arctan(\sqrt{3}) = 60^\circ $

Determining Polarization of Reflected Light

The given angle of incidence ($\theta_i$) is $60^\circ$. This is exactly equal to the Brewster's angle ($\theta_B$) calculated for this interface ($\theta_i = \theta_B = 60^\circ$).

At Brewster's angle:

• Unpolarized incident light is resolved into two components: one parallel and one perpendicular to the plane of incidence.
• The reflected light consists only of the component perpendicular to the plane of incidence.
• The component parallel to the plane of incidence is entirely transmitted into the second medium.

Therefore, when the angle of incidence is $60^\circ$, which equals the Brewster's angle, the reflected light is plane polarized perpendicular to the plane of incidence.