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Malus Light Intensity Law

When a beam of light, polarized by reflection at one plane surface is allowed to fall on the second plane surface at the polarizing angle the intensity of the twice reflected beam varies with the angle between the planes of the two surfaces. In the Biot’s polariscope it was found that the intensity of the twice reflected beam is maximum when the two planes are parallel and zero when the two planes are at right angles to each other. The same is also true for the twice transmitted beam from the polarizer and analyzer. The law of Malus states that the intensity of the polarized light transmitted through the analyzer varies as the square of the cosine of the angle between the plane of transmission of the analyzer and the plane of the polarizer. In the case of the Biot’s polariscope this angle is between the two reflecting planes.

The proof of this law is based on the fact that any polarized vibration may be resolved into two rectangular components: (i) parallel to the plane of transmission of the analyser (ii) at right angles to it.

Let OP = a be the amplitude of the vibrations transmitted or reflected by the polarizer and θ is the angle between the planes of the polarizer and the analyzer.

Resolve OP into two components,

(i) a cos θ along OA and

(ii) a sin θ along OB.

Only the a cos θ component is transmitted through the analyzer.

∴ Intensity of the transmitted through the analyser.

E₁ = (a cos θ)₂ = a² cos θ.

But E = a²

Where E is the intensity of incident polarized light

∴ E₁ = E cos² θ, and E₁ cos² θ

When θ = 0 i.e. the two planes are parallel

E₁ = E, because cos 0 = 1

When θ = π/2 the two planes are at right angle to each other.