Illustrated Physics
physics, drawn
Concept

Grazing incidence — where it appears

A wave meeting a surface almost parallel to it, at an angle of incidence close to ninety degrees. There every surface reflects completely and with the wave's sign reversed, so a source and its reflection cancel along the surface itself.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

A mirror for X-rays that works only at a glance. The fraction of 8 keV X-rays reflected by a smooth surface of gold and of silicon, against the grazing angle between the ray and the surface, in milliradians, with absorption included (solid) and without it (dashed). Below the critical angle √(2δ) — 10.02 mrad (0.57°) for gold, 3.88 mrad (0.22°) for silicon — the X-rays are totally reflected from outside the material, because its index is below the vacuum's; above it almost nothing is. Absorption rounds the edge and keeps the plateau a little below one. A mirror for X-rays is therefore a surface met at less than a degree, and it reflects well only while it is met that way.

The index that falls below one

Glass bends light because light is slower in it. X-rays are not slower in glass, or in anything: every material's refractive index for them is slightly less than one, by a few parts in a million. Everything about X-ray optics follows from that small number with the wrong sign. A lens that focuses them must be thinner in the middle than at the edges, and so weak that dozens are stacked in a row. A mirror reflects them only if they arrive at a glancing angle of less than a degree — totally, from the outside, the reverse of the way a diamond traps light — which is why the mirrors of an X-ray telescope are long, nested barrels rather than dishes.

optics · Refraction A signal that fades as the fourth power of distance. Received power, in decibels relative to free space at one metre, against distance on a logarithmic scale, for a 900 MHz transmitter 30 m up and a receiver 1.5 m up over flat, perfectly reflecting ground, with the ground's reflection taken as −1; dashed, free space alone, falling 20 dB per decade. Close in, the direct and reflected waves beat as their path difference passes through whole wavelengths. Beyond the break distance 4hₜhᵣ/λ = 540 m, the path difference 2hₜhᵣ/d is less than half a wavelength and shrinking, and the reversed reflection cancels the direct wave more and more completely: the power falls 40 dB per decade, as d⁻⁴, 10 dB below free space at ten times the break and 30 dB below at a hundred times. The ground, which was supposed to add a second path, takes the signal away; raising either antenna, which lengthens the path difference, is the remedy, and is why masts are tall.

The surface that cancels whatever skims it

Glass reflects four per cent of light falling straight on it, and water at radio frequencies two-thirds of the wave's amplitude. Tilt either towards grazing and the difference disappears: every surface, whatever it is made of, reflects a wave that only skims it completely, and turns it upside down. A wave travelling along a surface therefore meets its own reflection reversed and cancels on the surface itself. That one limit explains a dark fringe Humphrey Lloyd saw with a single mirror in 1834, why a mobile signal over flat ground fades with the fourth power of distance rather than the second, why a radar above the sea is blind at the horizon, and how a cliff in Sydney became the first radio interferometer.

optics · Refraction

Named alongside it

The objects these essays reach for when they reach for this one.

Brewster's angleCompound refractive lensCritical angleFresnel equationsInterferenceInterferometerLloyds mirrorPhase reversalPhase velocityPlasma frequencyRefractive indexTotal internal reflection

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