Concept

Refraction — where it appears

The bending of a ray as it crosses between two media of different refractive index, by Snell's law. It is the departure this collection measures against a pinhole: a bundle of refracted rays has no common centre, so a picture taken through water or glass is a projection of nothing from nowhere.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

00.2000.4000.6000.800204060how far off the axis the ray leaves the pinhole (°)how far the dome bends it (°)10 cm dome20 cm domeboth at offset/radius = 0.060identical to 1e-16°

The dome knows its offset in units of itself

A dome port centred on the entrance pupil bends nothing at all, exactly. One that is not bends rays by an amount that depends on the decentring over the radius and on nothing else, so a ten-centimetre dome six millimetres off centre and a twenty-centimetre dome twelve millimetres off centre are the same instrument, bit for bit. The picture carries the ratio, which means it never carries the radius.

refraction · Port
correct from 15 cm, at 160 mm widereflecting and refracting · 6.0e-12 px

One surface, two images

A water surface reflects what is above it and refracts what is below it in the same photograph, from the same plane. The reflected half has a centre of projection to 1 × 10⁻¹⁴ m and every theorem about central projection applies to it; the refracted half misses its own best-fitting point by 28.6 mm and none of it does. And the landscape manual's rule for drawing a reflection turns out to be the epipole placed at infinity, which is why it costs nothing at zero tilt and 11.5 px at twenty-two degrees.

refraction · Mirror
parallel in, no common point out18.6 mm of spread

A ball of water has no eye either

A flat interface is not a projection through a centre and misses by ten millimetres. A sphere of water misses by more than that on a ball the size of a plum — 1.3 mm on a fifty-millimetre radius, and the axis crossings spread over 18.6 mm at seven tenths of the aperture. But at two per cent of the radius the same fit returns 24 nanometres, so a ball does have a centre — one at zero aperture and none by the time it is gathering any light.

refraction · Nocentre
paraxial pupilthe stopa curved front elementcrossings 15.0 · 14.5 · 13.5 · 11.6 mm

The entrance pupil walks with the angle

The place a picture is a projection from is not a point in a wide-angle design. Chief rays traced through a strongly curved front element cross the axis 15.07 mm behind its front vertex when they are nearly on the axis, and 4.23 mm nearer the front at 80° of field. So no pivot makes a wide panorama seam clean: at one metre, pivoting at the paraxial pupil leaves 4.39 arcminutes of misregistration along a seam, and the best pivot still leaves 1.41.

lens · Pupil
eyethe stickcorrect from 18 cm, at 160 mm widerays miss by 3.13 mm

The stick a stereo pair puts back

Two eyes side by side reconstruct a submerged stick exactly as the sagittal image — kinked 14.96° — and two eyes one above the other exactly as the tangential one, kinked 9.59°. Roll the baseline between them and the two rays to a point miss each other by up to 3.13 millimetres, past the 2.85 a pixel covers at that range, and the reconstruction is a third stick that is neither — 551 millimetres of a one-metre stick, with its tip at 0.405 metres against a true 0.866.

refraction · Refraction

Named alongside it

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

centre of projectionSnell's lawNot a projectionApertureApparent-depthEntrance pupilinstrument limitleast-squares intersectionAstigmatismBaselineCausticChief ray

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