Illustrated Physics
physics, drawn
Concept

Mie scattering — where it appears

The scattering of light by a sphere comparable in size to the wavelength, solved exactly as a sum of spherical waves. It peaks sharply forward, depends only weakly on colour, and is why haze, cloud and fog look white or grey where small molecules make the sky blue.

Named by 3 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 How a dark ridge fades into the sky. The apparent contrast against the horizon sky of a black ridge at a given distance, seen in green light (550 nm) along a level path at sea level, on a logarithmic scale: e^(−βx), the light from the ridge scattered out of the path and the sky's light scattered in. The dashed line is the eye's threshold, a contrast of 2%. Clean air: β = 0.0116 per km, visible to 337 km; light haze, 0.05 per km: β = 0.06 per km, visible to 64 km; haze, 0.3 per km: β = 0.31 per km, visible to 13 km. Pure air sets a limit of a few hundred kilometres to how far anything can be seen; in practice haze shortens it to tens.

How far the air lets a mountain be seen

A dark mountain on the horizon fades not because its light grows too faint to see but because the air between it and the eye glows. Sunlight scattered into the line of sight fills the dark ridge in until it matches the sky behind it, and its contrast falls as a simple exponential of the distance. With the eye's threshold at two per cent, that gives a visual range of 3.912 divided by the air's scattering coefficient: about 337 kilometres for perfectly clean air in green light, far less in the hazes real air carries. The same arithmetic makes near ridges blue and far ones pale.

optics · Scattering The rings the full solution finds. The light scattered back by water drops of about 10 µm radius, at 550 nm, from the exact Mie series with around 134 terms for each drop, averaged over a ten per cent spread of sizes so that the fine ripple each single drop has is washed out. Instead of the smooth, weak background of the ray picture, the intensity rises sharply toward 180° through a series of rings about one and a half degrees apart, each brighter than the last, to a first ring 1.5° from straight back. These are what an observer sees round the shadow of an aircraft on a cloud, or round a shadow on a mist at a mountain top: the glory. It is present in the same mathematics that gives the rainbow, and it takes the whole series, with its surface-wave terms, to find.

The rings no ray can reach

Look down from an aircraft at a cloud, and round the aircraft's shadow there may be coloured rings, centred exactly on the point opposite the Sun. Mountain climbers have seen them round their own shadows for centuries, and every drop in that cloud is a sphere of water. Yet ray optics says that a drop of water cannot send light straight back. Its best ray falls fourteen degrees short. The glory lives entirely in those fourteen degrees.

optics · Scattering

Named alongside it

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

ExtinctionRayleigh scatteringAerial perspectiveAerosolAsymmetry parameterBackscatterCloud dropletContrastDimensionless numberDipole radiationGeometric opticsGlory

All concepts