Back to course
82WavesCore

Polarisation

A polarised\textbf{polarised} wave oscillates in only one plane. Ordinary light oscillates in every direction perpendicular to its travel, but passing it through a polarising filter selects just one. Because only transverse waves can be polarised, this simple effect is decisive evidence about what light is.

30 min Topic 5 · Waves and the Particle Nature of Light

What you'll be able to do

  • Explain what is meant by plane-polarised light
  • Describe the effect of a polarising filter and of crossed polarisers
  • Explain why polarisation shows light is a transverse wave
  • Describe applications including glare reduction and stress analysis
1

Plane polarisation

In unpolarised\textbf{unpolarised} light the electric field oscillates in all directions perpendicular to the direction of travel, changing rapidly and randomly.

A polarising filter\textbf{polarising filter} transmits only the component of oscillation along its transmission axis. What emerges is plane-polarised\textbf{plane-polarised}: its oscillation is confined to one plane, containing the direction of travel.

An ideal filter transmits half the intensity of unpolarised light, since on average half the oscillation lies along its axis.

I=12I0I = \tfrac{1}{2}I_{0}
Unpolarised light through one ideal polariser.
2

Two filters: the analyser

Pass polarised light through a second filter — the analyser\textbf{analyser} — and rotate it. When its axis is parallel to the light’s plane, maximum intensity passes. As it rotates, the transmitted intensity falls.

When the two axes are at 90∘90^{\circ} — crossed polarisers\textbf{crossed polarisers} — no light passes at all, because the analyser blocks exactly the plane the first filter let through.

Rotating the analyser through a full turn produces two maxima and two minima, at 180∘180^{\circ} intervals.

I=I0cos⁡2θI = I_{0}\cos^{2}\theta
Malus’s law — intensity through the analyser.
Example 1Polarised light of intensity 80 W m−280\ \mathrm{W\,m^{-2}} meets an analyser at 60∘60^{\circ} to its plane. Find the transmitted intensity.
1I=80cos⁡260∘=80×0.25I = 80\cos^{2}60^{\circ} = 80 \times 0.25.
Answer20 W m−220\ \mathrm{W\,m^{-2}}

Tip — Intensity follows cos⁡2θ\cos^{2}\theta, not cos⁡θ\cos\theta, because intensity depends on amplitude squared and only the cos⁡θ\cos\theta component of amplitude gets through.

3

Evidence that light is transverse

A longitudinal wave oscillates along its direction of travel — there is only one possible oscillation direction, so there is nothing for a filter to select between. Longitudinal waves cannot be polarised.

Light can be polarised, and crossed polarisers can extinguish it completely. That is only possible if its oscillation is perpendicular to its travel, so light must be a transverse wave.

Sound cannot be polarised, consistent with it being longitudinal. Microwaves can be polarised by a metal grille, confirming they are transverse too.

Tip — In an explanation, name the property that longitudinal waves lack: a choice of oscillation direction perpendicular to travel.

4

Applications

Light reflected\textbf{reflected} from water, glass or a road surface is partially polarised, mostly horizontally. Polarising sunglasses\textbf{Polarising sunglasses} with a vertical transmission axis block much of that reflected glare while still transmitting light from other sources.

Stress analysis\textbf{Stress analysis}: many transparent plastics rotate the plane of polarised light by an amount that depends on internal stress. Viewed between crossed polarisers, a stressed model shows coloured fringes, concentrated where stress is greatest — letting engineers find weak points before building.

LCD screens\textbf{LCD screens} place a layer of liquid crystal between crossed polarisers. An applied voltage changes whether the crystal rotates the plane of polarisation, switching each pixel between light and dark.

Photographers use polarising filters to darken skies and remove reflections; broadcasters polarise radio and TV signals, which is why aerials must be aligned.

Example 1Explain how polarising sunglasses reduce glare from a wet road.
1Light reflecting off the horizontal road surface is partially plane-polarised horizontally.
2The lenses have a vertical transmission axis.
3Horizontally polarised glare is largely absorbed, while unpolarised light from the scene is only halved.
AnswerThe lenses block the horizontally polarised component that dominates reflected glare.

Tip — Stress-analysis answers should mention crossed polarisers, the plastic rotating the plane of polarisation, and fringes being closest where stress is highest.

Equation recap

I=12I0I = \tfrac12 I_{0}
Unpolarised through one filter.
I=I0cos⁡2θI = I_{0}\cos^{2}\theta
Malus’s law.
θ=90∘⇒I=0\theta = 90^{\circ} \Rightarrow I = 0
Crossed polarisers.

Common mistakes to avoid

Saying sound can be polarised.
Sound is longitudinal, so it cannot be polarised.
Using I=I0cos⁡θI = I_{0}\cos\theta.
Intensity follows cos⁡2θ\cos^{2}\theta (Malus’s law).
Claiming a polariser transmits all of unpolarised light.
An ideal polariser transmits half the intensity.
Stating polarisation proves light is a particle.
It shows light is a transverse wave.

Key takeaways

  • Plane-polarised light oscillates in one plane only.
  • A polariser halves unpolarised intensity; crossed polarisers give zero.
  • Through an analyser, I=I0cos⁡2θI = I_{0}\cos^{2}\theta.
  • Only transverse waves can be polarised, so polarisation proves light is transverse.
  • Applications include glare-reducing sunglasses, stress analysis and LCD screens.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

Browse practice topics

Related lessons

All 11 lessons