Question

Explain what is meant by polarisation and derive Malus Law.

Answer 1

Hint: Polarization is defined as a phenomenon which is caused due to the wave nature of electromagnetic radiation. It has a definite direction which is relative to the direction of propagation of light.
The intensity of the polarised light is proportional to the square of cosine of angle between polarizer and the analyzer.
With the help of polarization only we can prove malus law.

Complete step by step answer:
Polarisation is a property of certain electromagnetic radiation where the direction and magnitude of the vibrating electric field are related to each other. The direction of polarization is defined to be the direction parallel to the electric field of the electromagnetic wave.
There are the type of polarization
Linear polarization
Circular polarization
Elliptical polarization
Malus Law:
This law states that when unpolarised light passes through a polarizer the that plane polarized light passed thought a analyzer then that light coming from an analyzer is proportional to the square of the cosine angle between polarizer and analyzer.
Mathematically represented as
$I\propto {\cos ^2}\theta $
Where,
I= Intensity
$\theta $ = Angle between polarizer and analyzer
To understand this consider a polarizer which is having its plan of transmission along a vertical direction. Now an ordinary light or an unpolarized light falls on the polarizer, out of that we will get a plane polarized light. Here the direction of the electric field is in a vertical plane. This plane polarized light falls on the analyzer, where the analyzer is basically a polarizer. Where the analyzer is rotated to a certain angle which shows the plane of transmission of the analyzer. Hence the angle between the polarizer and analyzer is $\theta $ .
Out of this analyzer we will get a plane polarized light but there will be two changes that take place here first the direction of vibration will change here that is the incident light is travelling along vertical direction while the emerging light is vibration along some different direction.
Second change is that the intensity of the emerging light will change. This change is due to Malus Law.
Let ${I_0}$ be the intensity of the light which is falling on the analyzer and $I$ be the intensity of the light that is coming out of the analyzer.
Then according to Malus law
$I = {I_0}{\cos ^2}\theta $
Draw a vector diagram having angle $E$ and ${E_1}$ is $\theta $ .
E= Vertical electric field of incident light
The analyzer split that electric field into two perpendicular component
One component will be parallel to the analyzer plane transmission which is the 1st component of the electric field of and the other will be perpendicular to the second component of the electric field.
$E = {E_1} + {E_2}$
$\cos \theta = \dfrac{{{E_1}}}{E}$
Therefore rearranging the terms we get
${E_1} = E\cos \theta $
Squaring both the sides we will get,
${E_1}^2 = {E^2}{\cos ^2}\theta $
We the relation between intensity and amplitude square.
So
${E_1}$ is the amplitude of the light that is coming out of the analyzer. Its square is directly proportional to the intensity $I$.
$E$ is the amplitude of the light that is incident on the analyzer it square is directly proportional to the intensity ${I_0}$ .
And therefore we can write
$I = {I_0}{\cos ^2}\theta $
Hence proved.

Note:
The incident plane light that is coming out of a polarizer and the emerging plane light from an analyzer are both plane polarized light but both of them do not lie in the same plane as the polarizer and analyzer has an angle of $\theta $ in between them.