Question

Unpolarized light in vacuum is incident onto a sheet of glass with index of refraction n. The reflected and refracted rays are perpendicular to each other. Find the angle of incidence. This angle is called "Brewster's angle" or "the polarizing angle". In this situation, the reflected light is linearly polarized, with its electric field restricted to be perpendicular to the plane containing the rays and the normal. (Answer in terms of n.)

Answer 1

Answer: $\theta_{B}=tan^{-1} n$

Explanation:

The situation described here is known as polarization by reflection. This was discovered by Scottish physicist David Brewster and then formulated the law that bears his name.

This polarization happens when the light incides at a specific angle, called the Brewster angle ($\theta_{B}$), which is given by the following formula (taking into account that generally the magnetic permeabilities of the two media involved do not vary):  

$tan\theta_{B}=\frac{n_{2}}{n_{1}}$ (1)

Where $n_{2}=n$ is the index of refraction of the second medium (the sheet of glass in this case) and $n_{1}=1$ is the index of refraction of the first medium (the air).  

Then:

$tan\theta_{B}=\frac{n}{1}$ (2)

Finding $\theta_{B}$:

$\theta_{B}=tan^{-1} n$ (3)