Diffraction and polarisation

Diffraction: waves bend round obstacles and spread after passing through an opening. Sound diffracts round doors easily because its wavelength is large. Light's wavelength is tiny, so its diffraction shows only with very small openings.

Single slit of width a: light gives a bright, broad central maximum, with dimmer bands on either side. The minima (dark bands) are at:

a sin θ = nλ (n = 1, 2, 3, ...)

Example: a = 0.1 mm, λ = 500 nm. The first minimum is at sin θ = λ/a = 5 × 10⁻³, so θ ≈ 0.005 rad. The central maximum spreads out to that angle on each side, so it is twice as wide as the other bands.

A narrower slit gives more spreading. Diffraction also blurs the images in microscopes and telescopes and limits how close two points can be and still be seen apart: their resolving power. Wider lenses or mirrors resolve finer detail.

Polarisation: in ordinary (unpolarised) light, the electric field vibrates in all directions across the ray. A polaroid sheet lets through only the vibration along one direction, its pass axis. The light that comes out is plane polarised.

Only transverse waves can be polarised. Sound, a longitudinal wave, cannot. So polarisation proves that light is a transverse wave.

An unpolarised beam through one polaroid loses half its intensity. A second polaroid at angle θ to the first passes:

I = I₀ cos²θ (Malus's law)

• θ = 0: all of it passes. θ = 60°: a quarter. θ = 90° (crossed polaroids): nothing.

Uses: polaroid sunglasses cut glare, because light reflected from water and roads is partly polarised. Light from the blue sky is also partly polarised, by scattering.