Radio diffraction
A Socratic walk-through of radio diffraction — reasoned out one step at a time, not lectured.
The question we started with
THE QUESTION #Why can a radio signal reach around a hill when light from the same direction cannot?
Drive into a valley with a ridge between you and the transmitter. The view of the mast is gone entirely — there is a hillside where it used to be. Yet the AM station keeps playing, while a microwave link on the same bearing would be stone dead. Light and radio are the same phenomenon, differing only in wavelength. So why does one of them get round the hill?
Reasoning it through
REASONING #Start with the thing that differs, since it is the only thing that differs. AM broadcast wavelengths run from roughly 180 to 560 metres. FM broadcasting is around three metres. A microwave link at 10 GHz is three centimetres, and visible light is a fraction of a micrometre. So the ridge is, to the AM wave, an object of about its own size — and to light, an obstacle some ten billion wavelengths across.
Why should that ratio matter? Think about what a wavefront is doing. Treat every point on it as a source of new wavelets spreading outward; the wave you observe next is what those wavelets add up to. In open space the sideways contributions cancel and the wave marches straight on. Put an edge in the way and you remove the contributions that would have cancelled the sideways spread — so behind the obstacle the wave does not stop at a sharp geometric line. It leaks in.
How far? The volume that actually carries a signal between two points is not a pencil-thin ray but an elongated ellipsoid, the first Fresnel zone, whose radius grows with the square root of wavelength times distance. For a long wave over kilometres that zone is hundreds of metres across, so a ridge poking into it obstructs only a fraction of the contributing energy. For light the zone is smaller than the objects around it, and an obstacle takes essentially all of it. The shadow is sharp because the wavelength is tiny, not because light travels differently.
So diffraction over the ridge is real, and it is the honest answer to the question as asked. But it would mislead to stop there, because for AM radio it is usually not the main thing bringing the signal in.
The first of the other two mechanisms is the ground wave. A vertically polarised wave at these frequencies couples to the conducting earth and follows its surface, curving with it — which is why AM stations use tall vertical masts as radiators rather than pointing beams at anything. Range depends on ground conductivity, so the same power reaches much further over seawater than over dry rocky terrain.
The second explains why the band changes character after dark. The lowest ionospheric layer, the D layer, is heavily absorbing at medium frequencies. During daylight it soaks up any signal heading upward, so what you hear by day is essentially all ground wave. At night the D layer's ionisation recombines and it effectively disappears; signals now pass through to the higher layers and refract back to earth far away. That is why distant stations crowd the dial after sunset — not because propagation is generally better in the dark, but because one absorbing layer has gone.
Then why not run everything at long wavelengths? Two reasons, both about size. Bandwidth is a fraction of carrier frequency, so a band centred at one megahertz has not the room for many channels or much information per channel. And antenna dimensions scale with wavelength — an efficient radiator for a 300-metre wave is an engineering project, while one for a 3-centimetre wave fits in a phone. Microwave links accept sharp shadows in exchange for capacity and small hardware, and pay for it with repeaters on hilltops.
The analogy
THE ANALOGY #Think of ocean swell meeting a harbour wall. Long, slow swell wraps around the end of the wall and reaches boats moored well inside the shelter. Short, choppy wind-waves of the same height stop dead at the wall and leave a genuinely calm patch behind it. Same water, same wall — only the wavelength differs, and it decides whether the wall casts a shadow at all.
Water waves are confined to a surface and slow down in shallow water, which bends them by refraction in ways radio over terrain does not copy, so the analogy shows why size ratio governs shadowing but not what happens to a radio wave's polarisation or its interaction with the ground's conductivity.
Clarifying the model
THE MODEL #Three refinements are worth pinning down.
Diffraction is not reflection or refraction, though popular accounts blur all three into "bending". Diffraction is the wave filling in behind an edge because the obstruction removed the cancelling contributions. Refraction is a gradual change of direction where propagation speed varies — what the ionosphere does, bending a skywave back down rather than mirroring it. Reflection is what a conducting surface does. Real coverage into a valley is a sum of several of these, plus scattering off terrain and buildings.
Diffraction is also not free. The signal behind the ridge is attenuated, and the loss grows with how far into the shadow you are and how sharply the obstacle intrudes into the Fresnel zone. "Reaches around the hill" means "arrives weakened but usable".
One correction worth stating: it is tempting to say low frequencies "penetrate" obstacles better and leave it there. Penetration through a material and diffraction around an obstacle are different mechanisms with different dependencies — both tend to favour longer wavelengths, but conflating them misleads about buildings, where material and thickness matter as much as frequency.
A picture of it
THE PICTURE #How to readRead top to bottom as one transmission followed through time, with the two notes marking day and night. The first pair of arrows is the mechanism that works around the clock — the ground wave hugging the earth and diffracting past terrain — and it is what you hear in the valley. The crossed arrow returning to the transmitter marks energy lost: by day the D layer absorbs the upward signal, so nothing distant arrives. After sunset that layer fades, the same energy reaches the F layer instead, and the final arrow is the skywave landing far beyond the ground wave's range. Nothing about the transmitter changed between the halves.
What became clearer
WHAT CLEARED #The hill is not an obstacle in any absolute sense — it is an obstacle relative to a wavelength. At AM wavelengths the ridge is comparable to the wave itself, so energy fills the shadow behind it; at optical wavelengths the same ridge is astronomically large and the shadow is sharp. That one ratio explains why long waves forgive terrain and microwave links demand a clear line of sight. But the distant AM station you find at midnight owes little to that ridge: it arrived by ground wave and, once the absorbing D layer dissolved after dark, by refraction from the ionosphere.
Where to go next
ONWARD #- How Fresnel-zone clearance is used quantitatively when siting a microwave link.
- Why HF bands used for long-distance communication behave almost opposite to MF across day and night.
Key terms
TERMS #| Term | What it means |
|---|---|
| Diffraction | the spreading of a wave into the geometric shadow of an obstacle, significant when the obstacle is comparable to the wavelength. |
| Fresnel zone | the ellipsoidal region around the direct path that carries most of the signal energy; its radius grows with wavelength and distance. |
| Ground wave | a surface-following mode at low and medium frequencies, dependent on the conductivity of the terrain. |
| Skywave | a signal refracted back to earth by the ionosphere, allowing propagation far beyond the horizon. |
| D layer | the lowest ionospheric layer, strongly absorbing at medium frequencies by day and largely absent at night. |
Every term the collection defines is gathered in the glossary.