How much each colour is scattered

At its defaults it draws how much each colour is scattered. Scattering strength against wavelength, as the inverse fourth power, normalised to one at 550 nanometres. Light at 450 nanometres is scattered 4.35 times as strongly as light at 650 nanometres — which is the whole reason the sky is the colour it is.

scattering-spectrum is one function in lib/figures/optics.js — rays, lenses, mirrors and what light does to a surface. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

Scattering strength against wavelength, as the inverse fourth power, normalised to one at 550 nanometres. Light at 450 nanometres is scattered 4.35 times as strongly as light at 650 nanometres — which is the whole reason the sky is the colour it is.

The transmitted amplitude behind a thin scatterer, drawn as a phasor: the incident wave of unit length along the axis, plus a forward-scattered wave of length 0.12 at 0°, 60°, 90°, 150°. What a detector reads is the square of the total length. A scattered wave along the incident one lengthens or shortens the sum in proportion to itself; one at right angles changes the length only in second order, because a small perpendicular addition to a long vector barely alters its length. So a scatterer that removes energy from the beam at first order must scatter forward with a component perpendicular to the incident wave, and the size of that component is the whole extinction — which is the optical theorem.

The extinction efficiency of a sphere of refractive index 1.33 — the light it removes, divided by what its geometrical shadow would remove — against its size in units of the wavelength over two pi. A small particle removes far less than its shadow. A large one removes twice as much: half by the shadow itself and half by the light diffracted out of the beam at the shadow's edge, which is a wave effect with no ray counterpart at all. Between the two the efficiency overshoots to 3.17 at a size parameter of 6.2, because the wave through the middle of the particle and the wave round the outside come out in step and then out of step as the particle grows. That is interference between two parts of one beam, and it is why a haze of a particular droplet size is much whiter than a haze of any other.

How much a gas slows light, computed from the forward scattering amplitude of a single molecule, against how many molecules there are in a cubic metre. The refractive index is not a separate property: the transmitted wave is the incident wave plus everything scattered forward, and adding a small wave that is a quarter turn behind the incident one retards the sum without changing its size — which is exactly what a phase delay is. The same amplitude whose imaginary part gives the extinction gives, through its real part, the index. At the density of air at sea level this route predicts n − 1 = 2.785e-4, and a refractometer measures 2.780e-4.

Scattered intensity against the number of scatterers, both logarithmic, for two ways of adding the same amplitudes. The lower curve averages 400 draws of N unit amplitudes with independent random phases and grows as N^0.990; the upper one adds them in phase and grows as N². At 1000 scatterers the two differ by a factor of 1065. Nothing about the scatterers is different between the two — same number, same strength, same wavelength. Only the arrangement is, and it is worth three decades here.

The fraction of sunlight of each wavelength that reaches the eye after crossing 1, 3, 20 atmospheres, computed from a Rayleigh optical depth of 0.0973 at 550 nanometres scaled as the inverse fourth power of wavelength. Overhead, the mean wavelength of what arrives is 548 nanometres; at the horizon, after 20 atmospheres, it is 623 nanometres.

physicscheck asserts something about scattering-spectrum that could fail — it draws it and measures the result against a value reached some other way.

Across the library: 100 interrogated, 2 exercised only, 1 untouched, of 103. Read out of the gate's source by the gate's own two patterns — and the gate's last claim fails the build if that read disagrees with what it was handed while running.