Not a projection — where it appears
Named by 6 essays across 2 fields — each of them below, with the objects they name alongside it.
A curved mirror has no eye
A flat mirror is a second camera — reflect the eye in the plane and every line of sight passes through the reflected point, to 2.8e-12 mm. Curve the mirror and the point is gone. Over 20 cm of a mirror ball two metres across, the lines of sight miss their own best-fitting point by 2.8 mm, and by 52.9 mm on a ball half a metre across. What replaces the eye is not a worse eye; it is nothing.
Where the focus went
If the reflected rays do not meet at a point, they meet each other in pairs, and the curve they are all tangent to is what the mirror has instead of a focus. On a sphere of 1.6 m vertex radius it is 184.1 mm long and has a cusp; near the axis it sits at R/2, which is why a small enough spherical mirror passes for a good one. This is the bright shape in the bottom of a coffee cup, computed rather than admired.
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.
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.
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.
Closer than they appear, by a factor with a number in it
A wing mirror of one metre radius held eighty centimetres from the eye reports 1.30 metres for an object at sixty-four, because the image of anything distant sits half a radius behind the glass. The size such an object subtends reads as a distance 2.60 times the true one, and the factor is exactly one plus twice the eye's distance over the radius — so the warning is a number, and it is larger for the mirror that is further away.
Named alongside it
The objects these essays reach for when they reach for this one.
centre of projectionAstigmatismCausticleast-squares intersectionRay tracingReflectionRefractionSnell's lawApertureEnvelopeFocusinstrument limit