Question

For a glass plate as a polarizer with refractive index 1.633, calculate the angle of incidence at which light is polarized.

Answer 1

Use the expression for polarization according to Brewster’s law. This expression gives the relation between the refractive index of the medium which is being used as a polarizer and the angle of incidence for which the light incident on the polarizer gets polarized or angle of polarization.

Formula used:
The expression for polarization according to Brewster’s law is given by
$\mu = \tan {\theta _p}$ …… (1)
Here, $\mu$ is the refractive index of the medium which is used as a polarizer and ${\theta _p}$ is the angle of polarization for the incident light.

Complete step by step answer:
We have given that a glass plate is used as a polarizer for the polarization of light. The refractive index of the glass plate is 1.633. We have asked to determine the angle of incidence at which the incident light is polarized. The angle of incidence for which the incident light is polarized is known as the angle of polarization.

We can determine the angle of polarization for the incident light using equation (1).
Rearrange equation (1) for the angle of polarization.
${\theta _p} = {\tan ^{ - 1}}\left( \mu \right)$
Substitute 1.633 for $\mu$ in the above equation.
${\theta _p} = {\tan ^{ - 1}}\left( {1.633} \right)$
$\therefore {\theta _p} = 58.5^\circ$

Hence, the angle of incidence for which the incident light is polarized is $58.5^\circ$.

Note: The students should be careful while determining the tangent of inverse of the refractive index of the medium given in the question. If this value is not determined correctly, the final answer for the angle of polarization will be incorrect. The students can determine this angle of polarization in degrees as well as in radians. Since there is no unit mentioned for this angle, we have determined this angle in degrees.