Polarisation

Polarisation is the restriction of the oscillations of a transverse wave to a single plane. It provides definitive evidence that light is a transverse wave and has numerous practical applications.

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What is Polarisation?

An unpolarised transverse wave oscillates in all planes perpendicular to the direction of propagation. For example, light from a bulb has electric field oscillations in every direction perpendicular to the ray.

A polarised wave has oscillations restricted to a single plane containing the direction of propagation. This plane is called the plane of polarisation.

Key Fact: Only Transverse Waves Can Be Polarised

Longitudinal waves (such as sound) cannot be polarised because their oscillations are already in a single direction — along the direction of propagation. The fact that light can be polarised is direct evidence that light is a transverse wave.

Exam Tip: If asked for evidence that light is a transverse wave, state that light can be polarised, and only transverse waves can be polarised. This is the definitive proof.

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Methods of Polarisation

1. Polaroid Filters (Polarising Filters)

A Polaroid filter (such as Polaroid film) contains long-chain molecules aligned in one direction. These molecules absorb the component of the electric field oscillating parallel to the chains, transmitting only the component oscillating perpendicular to the chains. The transmitted direction is called the transmission axis.

When unpolarised light passes through a single Polaroid:

• The transmitted light is plane polarised.
• The intensity is reduced to half the incident intensity (I₀/2), because on average, half the light oscillates in the permitted direction.

2. Reflection

When light reflects off a non-metallic surface (e.g., glass, water) at a certain angle, the reflected light is partially polarised. At the Brewster angle, the reflected light is completely polarised.

3. Scattering

Light scattered by small particles (e.g., molecules in the atmosphere) is partially polarised. This is why polarising sunglasses reduce glare from the sky.

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Crossed Polaroids

If a second Polaroid filter (the analyser) is placed after the first (the polariser):

• When the transmission axes are parallel: maximum light passes through. Transmitted intensity = I₀/2 (from the first filter).
• When the transmission axes are perpendicular (crossed): no light passes through. The first filter polarises the light in one plane; the second filter blocks this plane completely.
• At intermediate angles: some light passes through, governed by Malus's law.

Demonstrating Polarisation

Rotate two Polaroid filters relative to each other while looking through both. The transmitted intensity varies from a maximum (axes parallel) to zero (axes crossed, at 90°). This can only be explained if light is a transverse wave.

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Malus's Law

When plane-polarised light of intensity I₀ is incident on a polarising filter (analyser) whose transmission axis makes an angle θ with the plane of polarisation, the transmitted intensity is:

I = I₀ cos² θ

This is Malus's law.

Angle θ	cos θ	cos² θ	Transmitted Intensity
0°	1.00	1.00	I₀ (maximum)
30°	0.866	0.750	0.75 I₀
45°	0.707	0.500	0.50 I₀
60°	0.500	0.250	0.25 I₀
90°	0.000	0.000	0 (no transmission)

Worked Example 1 — Plane-polarised light of intensity 8.0 W m⁻² passes through a polaroid filter whose transmission axis is at 35° to the plane of polarisation. Calculate the transmitted intensity.

I = I₀ cos² θ = 8.0 × cos² 35°

cos 35° = 0.8192

cos² 35° = 0.6711

I = 8.0 × 0.6711 = 5.4 W m⁻²