Illustrated Physics
physics, drawn
Concept

Albedo — where it appears

The fraction of incoming sunlight that a planet, cloud or surface reflects rather than absorbs. Earth's is about 0.3, roughly half of it from clouds, and with the Sun's flux it sets the temperature a planet must radiate at to stay in balance.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

The temperature a planet ought to be. Each body's measured surface temperature against the temperature at which it would radiate away exactly the sunlight it absorbs — computed from two numbers, the sunlight reaching it and the fraction it reflects, with no other property of the body used. Points on the diagonal are bodies the one-line argument gets right. the Moon: balance 270 K, surface 250 K, −20 K with no atmosphere; Mercury: balance 433 K, surface 340 K, −93 K with no atmosphere; Mars: balance 210 K, surface 210 K, +0 K; Earth: balance 255 K, surface 288 K, +33 K; Venus: balance 227 K, surface 737 K, +510 K. The airless bodies fall below the line rather than on it, and the reason is the fourth power: a surface running from noon heat to night cold radiates like its hottest parts and averages like its coldest, so a mean thermometer reading is lower than the temperature that matches the emitted flux. Mars, whose atmosphere is thin and whose surface is nearly isothermal by comparison, sits on the line. Everything with a substantial atmosphere sits above it, by tens of kelvin on Earth and hundreds on Venus, and always in the same direction. Nothing here explains why. What the figure fixes is the size and the sign of what has to be explained.

The height a planet is seen from

A body in sunlight settles where it radiates away what it absorbs, and that takes two numbers and one line of arithmetic. It gets the Moon right and Earth wrong by thirty-three kelvin. The correction is not that the atmosphere traps heat but that it moves the level space sees the planet from, and the rest is done by a lapse rate that is not a radiative quantity at all.

thermodynamics · Blackbody 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 How much darker a surface looks under a film of water. The diffuse reflectance of a surface covered by a thin film of clear water (solid), against its reflectance dry, with the dry value for comparison (dashed): (1 − Rₑₓₜ) a (1 − Rᵢₙₜ)/(1 − a Rᵢₙₜ), where the film traps and returns light that falls outside its escape cone. A bright surface of reflectance 0.9 falls to 0.77; a mid-grey one of 0.5 to 0.32, 64 per cent of its dry value; a dark one of 0.2 to 0.11, 54 per cent. Dark surfaces darken proportionally most, because each return trip costs them most; and a coloured surface grows more saturated, because the colours it absorbs are absorbed again on every return while the colour it reflects survives.

The sand that darkens when it is wet

Wet sand is darker than dry sand, a wet stone darker than a dry one, a splashed pavement darker in patches, and a wet white shirt turns grey and then see-through. Water is clear and absorbs almost nothing, so it cannot be adding darkness. What it does is change where the light goes. A film of water on a surface traps light that has been scattered back up, returning most of it for another chance to be absorbed. Water in the pores between grains replaces air with something closer to the grains' own refractive index, so each grain turns light aside less, and light wanders deeper before it gets out. Both lengthen the path, and on a longer path more light is absorbed by the material that was there all along.

optics · Scattering

Named alongside it

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

AbsorptionMultiple scatteringAsymmetry parameterAtmosphereBlackbodyCoherent backscatteringConvectionDiffusionEmissivityEnergy balanceEscape coneIndex matching

All concepts