Coaching Centre
Polarisation
Polarised and unpolarised light, polarisation as evidence that light is a transverse wave, ways of polarising light, Malus's law I = Imax cos²θ, an investigation with a light sensor, and applications from sunglasses to phone screens.
Put on a pair of polarising sunglasses and look at your phone. Now tilt your head sideways. On many phones the screen fades almost to black, then returns as you keep turning. Nothing about the phone changed. The light leaving the screen vibrates in one particular direction, and your sunglasses only let through vibrations in another. That simple test is the strongest evidence that light is a transverse wave.
Light is a transverse wave
In a transverse wave the vibrations are perpendicular to the direction of travel. Light is an electromagnetic wave, and the vibrating quantity is the electric field (with the magnetic field perpendicular to it, 7A). The electric field could point in any direction at right angles to the beam.
- Unpolarised light, such as sunlight or light from a globe, is a jumble of waves from countless atoms, with electric fields in every direction perpendicular to the beam, changing randomly.
- Plane-polarised (linearly polarised) light has its electric field vibrating in just one plane.
Only transverse waves can be polarised. A longitudinal wave such as sound vibrates along its direction of travel, so there is no "sideways" direction to choose. This is why the discovery of polarisation forced Fresnel to treat light as a transverse wave, and why Huygens' longitudinal waves could not explain it.
Ways to polarise light
- Polarising filters. Edwin Land invented Polaroid sheet in 1929; the modern version (1938) contains long-chain molecules all lined up in one direction. Electrons can move along the chains, so they absorb the electric field component parallel to the chains. The component perpendicular to the chains passes through. That direction is the filter's transmission axis.
- Reflection. Light reflected from water, glass or a road is partly polarised, mostly horizontally. At one particular angle (the Brewster angle, about 53° from the normal for water) the reflected light is completely polarised. Polarising sunglasses have vertical transmission axes, so they block this horizontally polarised glare.
- Scattering. Sunlight scattered by air molecules is partly polarised, most strongly at 90° from the Sun. Bees and some birds navigate using this pattern in the sky.
Malus's law
When unpolarised light meets an ideal polarising filter, exactly half the intensity passes, since on average half of each random field is along the axis. The light that emerges is polarised along the filter's axis.
When already polarised light meets a second filter (the analyser) whose axis is at angle $\theta$ to the light's plane of polarisation, only the component of the electric field along the new axis passes: $E = E_0\cos\theta$. Intensity is proportional to the square of the field amplitude, so
$$I = I_{max}\cos^2\theta$$
where $I_{max}$ is the intensity of the polarised light arriving at the analyser. Étienne-Louis Malus discovered polarisation by reflection in 1808 while looking at sunlight reflected from the windows of the Luxembourg Palace through a calcite crystal.
Useful values: $\cos^2 0^\circ = 1$, $\cos^2 30^\circ = 0.75$, $\cos^2 45^\circ = 0.5$, $\cos^2 60^\circ = 0.25$, $\cos^2 90^\circ = 0$.
Unpolarised light of intensity 80 W m⁻² passes through a polariser and then an analyser at 30° to it. Find the final intensity.
Two filters are crossed at 90°, so no light passes. A third filter is slipped between them with its axis at 45° to both. Unpolarised light of intensity 100 W m⁻² enters. Find the light that emerges.
Polarised laser light passes through an analyser and 20% of the intensity is transmitted. Find the angle between the analyser axis and the plane of polarisation.
Applications
- Sunglasses and camera filters cut glare reflected from water and roads, and darken the sky to bring out clouds.
- LCD screens sandwich liquid crystal between crossed polarisers. A voltage across each pixel changes how much the crystal rotates the plane of polarisation, which controls how much light gets through the second polariser. That is why the screen in the hook could be blacked out.
- 3D cinema projects the left-eye and right-eye images with different polarisations, and each lens of the glasses passes only one.
- Stress analysis. Clear plastics viewed between crossed polarisers show coloured fringes where they are under stress, so engineers test models of bridges and parts this way.
- With the lamp and the default filters crossed at 0° and 90°, confirm no light reaches the detector. Move the last filter to 30° and check the 37.5 W/m² reading with Malus's law.
- Turn the last filter slowly from 0° to 180°. How many times does the light go dark? Sketch intensity against angle.
- Set the filters crossed again, then Add a middle filter at 45°. Check the 12.5 W/m² against the worked example. Which middle angle lets the most light through?
- Switch to the laser (already polarised at 0°). Set filter 1 to 60° and the last filter to 60° as well. Explain the 25 W/m² reading.
- With the laser, why does filter 1 now matter at 0° but not with the lamp?
Test yourself
Polarisation provides evidence that light is
Only transverse waves have a sideways vibration direction that can be selected.
Polarised light of intensity 60 W m⁻² meets an analyser at 60° to its plane. The transmitted intensity is
$60\cos^2 60^\circ = 60 \times 0.25 = 15$ W m⁻².
Unpolarised light of intensity $I_0$ passes through three filters at 0°, 30° and 60°. The final intensity is
$\tfrac{1}{2}I_0 \times 0.75 \times 0.75 = 0.28I_0$.
Polarising sunglasses reduce glare from a lake because
Reflection polarises light parallel to the surface; vertical transmission axes block it.
Label the polarisation diagram
Order the arrangements from most to least transmitted light. Unpolarised light enters each.
An ideal filter transmits the intensity of unpolarised light. The direction a filter lets through is its transmission . Light reflected from a road is partly polarised . Only waves can be polarised. Two filters at 90° are said to be .
Two polarising filters are crossed so that no light passes. A student places a third filter between them and finds that light now passes. (a) Explain this observation. (b) If unpolarised light of intensity 120 W m⁻² enters and the middle filter is at 30° to the first, calculate the intensity that emerges.
(a) A polarising filter transmits only the component of the electric field along its transmission axis, and the light that emerges is polarised along that axis. With crossed filters, the light leaving the first filter has no component along the second filter's axis, so nothing passes. A middle filter at an angle passes part of the light and re-polarises it along its own axis, which is no longer perpendicular to the last filter. That light now has a component along the last filter's axis, so some passes.
(b) First filter: $I_1 = \tfrac{1}{2} \times 120 = 60$ W m⁻². Middle filter at 30°: $I_2 = 60\cos^2 30^\circ = 45$ W m⁻². Last filter is at 90° − 30° = 60° to the middle one: $I_3 = 45\cos^2 60^\circ = 11$ W m⁻² (11.25).