MALUS LAW

Explanation

Malus law. It states that the intensity of polarised light transmitted through the analyser varies as the square of cosine of the angle between the plane of transmission of analyser and polariser.
i.e. `I prop cos^(2) theta`
Proof
Let OQ = amplitude (A) of vibration of electric vector transmitted by the polariser.
`theta = "angle between the plane of analyser and polariser"`.
 Let us resolve `vecA` into two components.

(i) A `cos theta` along OR (i.e. parallel to the plane of transmission of analyser)
(ii) A `sin theta` along OP (i.e. perpendicular to the plane of transmission of analyser)
Since only A `cos theta` component is transmitted through the analyser, so the intensity of light transmitted through the analyser is given by :
`I = (A cos theta)^(2)`
or `I = A^(2) cos^(2) theta`
or `I = I_(0) cos^(2) theta`
where `I_(0)= A^(2)` is the intensity of incident light from the polariser.
So. Eq. (1) can be written as
`I prop cos^(2) theta`.
Special cases
(i) When the plane of polariser and analyser are parallel to each other.
i.e. `theta= 0^(@)`
 From Eq. (1), we have
`I=I_(0)`
i.e. maximum intensity.
(ii) When the plane of polariser and analyser are perpendicular to each other. From> i.e. `theta= 0^(@)`
From Eq. (1), we have
I = 0
i.e. zero intensity.