Concept

Prism — where it appears

A block of transparent material with inclined faces, which deviates light by refraction and spreads its colours because the index depends on wavelength. Pairs of prisms can also add a controllable dispersion to a light pulse, compressing it in time.

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

The deviation that has a bottom. The angle by which a 60° and a 90° ice prism bends a ray, against the angle at which the ray arrives, for an index of 1.31. Each curve is traced ray by ray through both faces and stops where it stops: outside the plotted range the ray meets the second face beyond the critical angle and never leaves. Both curves have a minimum, and the minimum is the point of the figure twice over. Its value — 21.84° for the 60° prism and 45.73° for the 90° prism — is where the sky puts a halo. And its flatness is why there is a halo at all: near a minimum the deviation changes only in second order, so a wide band of orientations all deliver light to nearly the same angle, and a cloud of randomly tumbling crystals piles up a bright ring there while sending the rest of the light nowhere in particular. The passage at the minimum comes out symmetric — in at 40.92°, out at 40.92° — which was found by searching the traced curve rather than assumed. The window of incidence that gets through at all is 76.5° wide for the 60° prism against 32.2° for the 90° one, a factor of 2.4, and that is why one of the two halos is common and the other is rare.

The ring at twenty-two degrees

A halo round the sun is a caustic in orientation rather than in space. Most of the ice crystals in a cirrus cloud send light nowhere in particular; the ones near minimum deviation all send it to nearly the same angle, because a minimum is flat — and the angle they pick has a red inner edge, which is the reverse of a rainbow.

optics · Dispersion $Colours that leave a grating on different roads. A pair of parallel diffraction gratings with 1,200 lines per millimetre and light arriving at 30°, drawn to scale for three wavelengths, 760, 800 and 840 nm. The first grating sends each colour off at its own angle — 24.3° for 760 nm, 27.4° for 800 nm, 30.5° for 840 nm — and the second turns them all back parallel to the input, side by side. Between the gratings the red travels the longest road: for gratings 10 mm apart the slant paths are 10.97 mm, 11.26 mm, 11.61 mm. Measured to a common wavefront after the second grating, the longer road still wins, so red arrives last: the geometry has given the pulse the opposite ordering to the one glass gives it.$

The dispersion made of angles

Glass delays blue light more than red, so a short pulse that passes through glass comes out stretched with its red end first. At the wavelengths where most short-pulse lasers work, no transparent glass does the opposite. Two diffraction gratings do it with no material at all. The first spreads the colours in angle, the second turns them back parallel, and in between the red has travelled the longer road. A spread in angle, however it is made, always adds this kind of dispersion, of the sign glass cannot give. It is how every high-power ultrafast laser squeezes its pulse back after amplifying it.

optics · Dispersion $A point of light split by an uncoated roof. The image of a distant point across the direction of the roof edge, behind an Amici roof in glass of index 1.517, for unpolarised light, as a fraction of the peak an undivided pupil would give, against position in units of the diffraction width λ/D: with a phase-coated roof, and with bare glass. The coated roof gives the ordinary diffraction pattern of the full aperture. Bare glass leaves the two halves of the pupil only partly able to interfere, and the image's peak falls to 0.70 of its proper height, its central lobe widening across the edge into a shoulder on each side — a slight doubling of every point, which an observer sees as a loss of crispness and contrast.$

The roof that splits a binocular's image

A slim, straight binocular turns its image upright with a roof — two glass faces meeting at a right angle, which reflect every ray twice by total internal reflection and lose no light at all. They lose sharpness instead. Total reflection shifts the phases of the two polarisations of light by different amounts, and the half of the beam on one side of the roof's edge meets the two faces in the opposite order from the other half. The halves leave in different polarisations, interfere only partly at the focus, and every star becomes a slightly doubled smudge — unless a coating a fraction of a micrometre thick makes the glass behave like a mirror.

optics · Total internal reflection

Named alongside it

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

Dispersion Total internal reflection Angular dispersion Caustic Chirped-pulse amplification Diffraction grating Diffraction limit Fresnel equations Group delay dispersion Group velocity Halo Ice crystal

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