Question

The refractive index of a material is \[\sqrt 3 \]. What is the angle of the refraction if the unpolarized light is incident on it at the polarizing angle of the medium?

Answer 1

Hint: The process of bending of the light rays is called refraction. The angle of refraction has a relationship with the polarization angle. The refractive index is equal to the tangent of the polarization angle. So the angle of refraction can be found using values of refractive index and polarization angle.

Complete answer:
A measure of the reduction in the velocity of light in the medium is the refractive index of a medium. The angle between the refracted ray and normal ray drawn at the point of incidence to the interface at which refraction occurs is the angle of refraction.
The process of bending of the light rays is called refraction. The refraction is caused because of the change in speed by light when it changes medium.
The angle of polarization is the angle at which the light is transmitted through a transparent medium with no reflection. The un-polarized light is incident at this angle, the light will be perfectly polarized.
Here, The refractive index \[\mu \]=\[\sqrt 3 \],
\[r = \]refractive angle.
If the relationship between polarization angle \[{i_p}\]and refractive index \[\mu \]is given by,
It \[{i_p}\]is the polarizing angle, then from
\[\tan {i_p} = \]\[\mu = \sqrt 3 \]
\[{\tan ^{ - 1}}\sqrt 3 = {60^ \circ }\]
\[{i_p} = {60^ \circ }\]
If the incident angle \[{60^ \circ }\]the angle of refraction \[r\]is obtained from
\[\mu = \dfrac{{\sin i}}{{\sin r}}\]
\[\sin r = \dfrac{{\sin i}}{\mu } = \dfrac{{\sin {i_p}}}{\mu } = \dfrac{{\sin {{60}^ \circ }}}{{\sqrt 3 }}\]
\[\sin r = \dfrac{{\sqrt 3 }}{{2\sqrt 3 }} = \dfrac{1}{2}\]
\[r = {\sin ^{ - 1}}\dfrac{1}{2}\]
\[r = {30^ \circ }\]
Hence, the angle of refraction is \[{30^ \circ }\].

Note: The bending of light that passes from one transparent substance into another substance is called refraction.
The refraction is a bending of the sun rays as they enter raindrops forming a rainbow.
The light travels from one medium to another. The frequency of light doesn’t change but the velocity and wavelength of light are changed.