Illustrated Physics
physics, drawn
Concept

Asymmetry parameter — where it appears

The mean cosine of the angle through which a particle scatters light: zero when it scatters equally in every direction, near one when it scatters strongly forward. Written g, it lets multiple-scattering calculations lengthen the step to ℓ/(1 − g), the distance over which a photon forgets its direction.

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

Where the sky's blue goes. How many times more strongly a sphere scatters 450 nm light than 650 nm light, against its radius, with the radius on a logarithmic axis running from a couple of nanometres to twenty micrometres. On the left the ratio sits at 4.35, which is the fourth power of the wavelength ratio and the whole reason the daytime sky is blue. It does not stay there. By a radius of 245 nm the preference has halved, and by a micrometre it has essentially gone: a particle comparable with the wavelength scatters every visible colour within a few per cent of equally, which is why a cloud is white, why fog is white, why milk is white and why the exhaust of a cold diesel is white while the smoke of a cigarette — whose particles are ten times smaller — is blue. Nothing about the material changed between one end of this axis and the other; only the size did.

When the particle is the size of the wave

The sky is blue because small things scatter short wavelengths far more strongly. A cloud is made of the same water and scatters every colour alike. Nothing about the material changed — only the size, and one dimensionless number crossing one.

optics · Scattering Light that walks through a cloud. Seven photons entering a slab 8 scattering mean free paths thick from above, straight down, and followed until they leave, with every scattering equally likely to send them in any direction; their paths are projected onto the page. Of 20000 photons followed the same way, 82.5 per cent come back out of the top and 17.5 per cent out of the bottom. Diffusion theory predicts 18.2 per cent through the bottom. Only 10 photons cross without scattering at all, where e⁻⁸ predicts 6.7 — within the counting error of so few: nearly all of what is transmitted has walked, and the direction it arrived from is forgotten on the way.

The cloud light has to walk through

A beam crossing thirty scattering lengths of anything should keep e⁻³⁰ of itself — a ten-millionth of a millionth. A cloud thirty scattering lengths thick lets through nearly a third of the sunlight falling on it. The light has not crossed; it has walked, one scattering at a time, and a walk through a slab obeys a law with the shape of Ohm's rather than of an exponential.

optics · Scattering

Named alongside it

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

Multiple scatteringAlbedoCoherent backscatteringDiffusionDimensionless numberDipole radiationExtinctionLimiting caseMean free pathMie scatteringOptical depthPhase function

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