Question

A transparent medium of the angle of polarization is ${{60}^{0}}$. Find the angle of refraction.

Answer 1

Hint: The sum of angle of polarization and the angle of refraction is equal to ${{90}^{0}}$. Angle polarization is also called Brewster's angle. The angle at which the light must be incident on the surface for the reflected light to acquire maximum plane polarization is called the polarization angle.

Formula used:
${{i}_{p}}+r={{90}^{0}}$

Complete answer:
Let us assume the angle of polarization as ${{i}_{p}}$and the angle of refraction as $r$. Now, we know, the sum of the polarization angle and the refraction angle is equal to ${{90}^{0}}$

On applying it to the above values,
$\begin{align}
  & {{i}_{p}}+r={{90}^{0}} \\
 & {{60}^{0}}+r={{90}^{0}} \\
 & r={{30}^{0}} \\
\end{align}$
Therefore, the angle of refraction is ${{90}^{0}}$

Additional Information:
Also called Brewster's angle, the angle of polarization is the angle at which light is transmitted through a transparent medium with no reflection. When the unpolarized light is incident at this angle, the light will be perfectly polarized. It is named after the physicist Sir David Brewster.
The physics behind this phenomenon can be understood easily by the way electric dipoles will respond to polarized light. Brewster’s angle for visible light is approximately ${{53}^{0}}$. As the refractive index of a given medium changes depending on the wavelength of the light, the Brewster’s angle will also vary accordingly to different wavelengths.

Note:
The polarization angle characteristics change according to the shape, size, and optical properties of the scattering plane. In general, the light is negatively polarized if it is on the scattering plane and is positively polarized if it is perpendicular to the scattering plane.