Question

State and explain Malus law.

Answer 1

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 ∝ cos² θ

Proof

Let OQ = amplitude \((\overrightarrow A)\) of vibration of electric vector transmitted by the polariser.

θ = angle between the plane of analyser and polariser.

Let us resolve \((\overrightarrow A)\) into two components.

• A cos θ along OR (i.e. parallel to the plane of transmission of analyser).
• A sin θ along OP (i.e. perpendicular to the plane of transmission of analyser).

Since only A cos θ component is transmitted through the analyser, so the intensity of light transmitted through the analyser is given by:

I = (A cos θ)²

or I = A² cos² θ

or I = I₀ cos²θ ...........(1)

where I₀ = A² is the intensity of incident light from the polariser.

So Eq. (1) can be written as I cos²θ.

Special cases

(i) When the plane of polariser and analyser are parallel to each other.

i.e. θ = 0°

From Eq. (1), we have

I = I₀

i.e. maximum intensity.

(ii) When the plane of polariser and analyser are perpendicular to each other.

i.e. θ = 90°

From Eq. (1), we have I = 0

i.e. zero intensity.