Question

State and obtain Malus’ law.

Answer 1

When a beam of plane polarised light of intensity I₀ is incident on an analyser, the light transmitted of intensity I from the analyser varies directly as the square of the cosine of the angle θ between the transmission axis of polarizer and analyser. This is known as Malus’ law.

I = I₀ cos²θ

Proof:

1. Let us consider the plane of polariser and analyser are inclined to each other at an angle θ.
2. Let I₀ be the intensity and ‘a’ be the amplitude of the electric vector transmitted by the polariser.
3. The amplitude ‘a’ of the incident light has two rectangular components, (acos θ) and (a sin θ) which are the parallel and perpendicular components to the axis of transmission of the analyser.
4. Only the component (a cosθ) will be transmitted by the analyser. The intensity of light transmitted from the analyser is proportional to the square of the component of the amplitude transmitted by the analyser.
5. I ∝ (a cos θ)² I = k(a cos θ)²
   Where k is constant of proportionality.
   
   Malus’s law
   

   I = ka² cos² θ
   I = I₀ cos² θ
   Where, I₀ = ka² is the maximum intensity of light transmitted form the analyser.

   
   

   Special cases:
   Case (i):
   When θ = 0°, cos 0 = 1, I = I₀

   Case (ii):
   When θ = 90°, cos 90° = 0, I = 0