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

Angular diameter — where it appears

The angle a source or an object subtends at a point, which for anything small is its size divided by its distance. It is what a penumbra's width records about a lamp: scale the lamp and its distance together and the angular diameter is unchanged, and so is the shadow.

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

source, 35 cmthe occluder's edgefraction of the source visiblepenumbra 17.5 cmprojection: 17.50 cmsampled: 17.41 cm

The penumbra is the lamp's image

The soft edge of a shadow is a picture of the light, projected through the occluder's edge as through a pinhole. That gives its width without any integration — and it is why the dapples under a tree go crescent-shaped during an eclipse.

light · Penumbra 18.0 cmcard at 1.00 m144.0 cmcard at 2.40 mrecovered: 36.0 cm at 3.00 mtwo cards, two bands, one lampcondition number 37.1

The lamp's size over its distance, and nothing else

One straight-edge shadow gives a lamp's angular size and nothing about its actual size or distance — scale a 36 cm lamp and its 3.0 m distance together and the band it casts differs by 0.0e+0. A second card at a different height breaks the tie, recovering 36.00 cm at 3.000 m from bands of 18.0 cm and 144.0 cm alone, at a condition number of 37.1.

light · Penumbra

Named alongside it

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

PenumbraUmbraArea lightConditioningDegeneracyleast squaresPicture planePinholeVanishing point

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