Visual Plane
every picture states the point it is correct from
Concept

Radiance — where it appears

The quantity a picture records of a surface: the area one pixel covers times the light per unit area reaching it, and therefore independent of distance. The two factors cancel exactly, which is why a wall does not get darker as the camera backs away and why this is a geometric statement rather than a photometric one.

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

00.50011020304050distance from the camera to the wall (m)relative to the value at 1 mthe patch, growing as d²the light per unit area, falling as 1/d²their product — what the picture records2500× the footprint at the far endproduct flat to 2e-16

A wall does not get darker as it goes away

The inverse square law is about a point source. A surface is not a point source, and the picture of a wall is exactly as bright at twenty metres as at two — the patch one pixel covers grows as the square of the distance and the light per unit area falls as the square of the distance, and a picture records the product. Which is why aerial perspective has to be the air.

light · Radiance 0204051015distance from the source to the ball, in radiifraction of the ball's surface that is lit (%)one half — the source at infinity25.0% at 2 radiicurve: the closed form · dots: quadratureagreeing to 5e-4

A lamp lights less than half a ball

Everyone knows a sphere is half lit. It is half lit by a source at infinity and by nothing else: a lamp two radii away lights a quarter of it, and the boundary it draws is a circle offset toward the light rather than a great circle. The offset is R²/D, which means a photograph of a lit ball carries the distance to whatever lit it.

light · Terminator 87.7% of the skycorrect from 16 cm, at 160 mm wide5.512 sr of 6.283

What a point in shadow can see of the sky

A place directly under a slab is not sealed off from the sky at all — it sees 83.4 per cent of it, 5.242 of the 6.283 steradians a place in the open has, against 5.240 from the closed form for a rectangle's own solid angle. The same counted-directions call that measures a lamp's penumbra measures this fraction too, and the two agree to 2.50e-4 with the source simply swapped from a lamp to the whole sky.

light · Ambient

Named alongside it

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

DemonstrationDepth cuePoint lightSubtended angleTerminatorcentre of projectionConicDiminutionfield of viewForeshorteningNormalisationPenumbra

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