Gap width, wavelength and how much waves spread

"Does a 2 cm gap diffract waves?" is the wrong question. What matters is the ratio of the gap width to the wavelength.

A 2 cm gap is tiny for a 10 m radio wave but enormous for a 0.0005 mm light wave, and the two cases behave completely differently.

So compare $w$ (gap width) with $\lambda$. There are three useful cases.

When $w \gg \lambda$, most of the wavefront passes straight through. The beam stays almost as wide as the gap and travels nearly straight ahead.

Behind the barrier there is a shadow region that is only slightly blurred at its edges. The wave bends a little into the shadow, but not much.

This is why a torch beam through a doorway stays a beam, and why light from a window makes a fairly sharp patch on the floor.

When $w \approx \lambda$, the spreading is at its most dramatic. The wavefronts leave the gap as semicircles and the wave fans out widely on the far side.

The gap now behaves like a small point source. The wave's energy is spread over a much larger region, so the amplitude away from the gap is smaller than it was in the beam.

This is the case examiners usually mean by "diffraction is greatest when the gap is comparable with the wavelength".

When $w < \lambda$, the wave spreads out through almost all of the region behind the barrier — it no longer looks like a beam at all.

But there is a catch: a very narrow gap lets only a small fraction of the wave's energy through. The transmitted wave is widely spread and weak.

So "narrower gap means more diffraction" is true for the angle of spreading, not for the intensity you receive.

A ripple tank shows this in real time.

1. A vibrating bar (a dipper) makes straight, parallel water waves of fixed wavelength.
2. Place a barrier across the tank with a gap in it.
3. Shine light from above so the wave crests cast shadows you can see (or project them).
4. Watch the wavefronts after the gap.

What to do: keep the dipper frequency — and so the wavelength — constant, and change only the gap width.

What you see:

• Wide gap: the wavefronts stay nearly straight; the beam continues with sharp-ish edges.
• Gap about one wavelength: the wavefronts become strongly curved semicircles.
• Narrower gap: the curvature spreads over a wider angle, and the pattern is fainter.

The control experiment: with the gap fixed, increase the frequency. The wavelength shortens, so the gap becomes "wide" compared with $\lambda$ and the spreading decreases.

Diffraction is not only about gaps. A wave passing the edge of an obstacle spreads into the region behind it.

Sea waves passing a harbour wall or a headland fan out into the sheltered water. Sound from a source hidden behind a building still reaches you. Radio waves of long wavelength reach valleys that are screened from the transmitter by hills.

The same rule applies: the longer the wavelength compared with the obstacle, the more the wave spreads into the "shadow".