Polarisation of light

Hold one end of a long horizontal string whose far end is fixed, and move your hand up and down periodically. A wave y(x, t) = a sin(kx − ωt) travels along +x, where a is the amplitude, ω = 2πν and k = 2π/λ.

The string moves along y while the wave travels along x, at right angles: a transverse wave. Because the displacement is along y it is called y-polarised. Each point moves on a straight line, so the wave is linearly polarised, and since the string stays in the x-y plane it is also called plane polarised.

Moving the hand in the x-z plane instead gives a z-polarised wave, z(x, t) = a sin(kx − ωt). Both are transverse and linearly polarised.

If the plane of vibration is changed at random over very short intervals, the wave is unpolarised. Its displacement keeps changing direction, but always stays perpendicular to the direction of travel.

Light is a transverse wave: its electric field always oscillates at right angles to the direction the light travels. Natural light, from the Sun or a sodium lamp, is unpolarised; its electric vector takes every direction in the transverse plane, rapidly and at random.

A polaroid is a thin plastic-like sheet containing long-chain molecules aligned in one direction. It absorbs the part of the electric field along the molecules and lets through the part perpendicular to them. That direction is the pass-axis.

So unpolarised light that passes through one polaroid comes out linearly polarised along the pass-axis, with half the incident intensity. Rotating that single polaroid leaves the transmitted intensity unchanged.

Polarisation is special to transverse waves. Longitudinal waves such as sound in air show interference and diffraction too, but they cannot be polarised.