Point source — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
How many lamps make one lamp
An array of point lamps spread across the width a real lamp would occupy leaves a staircase rather than a ramp — 4 lamps step by 25.0 per cent of the whole, 64 by 1.6 per cent — and the worst departure from the true ramp falls as the -1.007 power of the count. A single point lamp is not a coarse version of that staircase; it is wrong by 0.50, the most a fraction can be wrong by.
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.
Named alongside it
The objects these essays reach for when they reach for this one.
PenumbraUmbraArea lightNormalisationPower lawQuantisationRadianceShadow projectionSolid angle