Diffraction at a single slit

Look closely at the edge of the shadow of an opaque object and you will find alternate bright and dark bands just inside and outside it. This is diffraction, which every kind of wave shows: sound, light, water waves and matter waves.

The wavelength of light is much smaller than most obstacles, so diffraction of light goes unnoticed in daily life. It still sets the limit on how finely the eye, a microscope or a telescope can separate close objects, and it makes the colours seen on a CD.

Hearing someone talk from round a corner surprises nobody. Light also spreads a little beyond narrow holes and slits into the region that should be shadow; Newton and others noticed this before Young.

Set-up: a parallel beam falls normally on a slit LN of width a. M is its midpoint, and the line from M at right angles to the slit meets the screen at C. The lines from different parts of the slit to a point P on the screen are close to parallel and make an angle θ with MC.

Method: split the slit into many narrow strips and treat each as a source of secondary wavelets. The incoming wavefront is parallel to the slit, so all the strips start in phase; their contributions are added at P with the proper phase differences.

Result: a bright central maximum at θ = 0; zero intensity at θ ≈ nλ/a with n = ±1, ±2, ±3, ...; and secondary maxima near θ ≈ (n + ½)λ/a, each weaker than the one before as n grows.

The central maximum reaches from −λ/a to +λ/a, twice the angular width of each of the other bands. A narrower slit or a longer wavelength spreads the whole pattern wider.

For example, with λ = 600 nm and a = 0.1 mm the first minimum is at θ = (6 × 10⁻⁷)/(1 × 10⁻⁴) = 6 × 10⁻³ rad; on a screen 1 m away that is 6 mm from the centre, and the central band is 12 mm wide.