Concept

Pinhole — where it appears

6 essays name this object, across 3 fields. What follows is each of them, and the objects they name alongside it.
water, n = 1.333eyetruly 1.50 m downappears 0.818 m downh/n would be 1.125 mno single viewpoint — the rays miss by 17.1° of bend at the surfaceapparent depth 54.5% of the true one, not 75.0%

What a ray does at a surface

A pool looks three-quarters as deep as it is — but only if you look straight down. At sixty degrees the same bottom appears at half its depth, and at eighty at a fifth, which is why the far end of a pool looks shallow enough to walk in.

refraction · refraction
the water surfacethe pinholethe rays miss by 9.9 mmno single viewpoint — the rays miss by 9.9 mmdry control: 0e+0 m

A picture through water has no viewpoint

Continue the rays of a refracted picture into the water and fit them to a common point. They miss it by ten millimetres. The same fit with the water taken away misses by zero, which is what makes ten millimetres a measurement rather than a number.

refraction · nocentre
no single viewpoint — the rays miss by 4.5 px, depth-dependentf recovered from it: 396.88 px

What survives a pane of glass

A slab of glass moves every point of a picture and moves no direction at all. So the camera recovered from a photograph taken through a display case is exactly the camera that took it — out of a picture in which nothing is where it was.

refraction · slab
the panelhorizon — the centric point's heightthe section — the eye, the panel, the ground470 px — the viewing distancethree routes agree to 6e-14 pxsection, distance point, and a pinhole camera

Alberti draws a pavement, and chooses where the reader stands

The costruzione legittima of 1435 is exact. Run as a construction — with drawn rays and drawn intersections rather than the formula it turns out to satisfy — it agrees with a pinhole camera to six parts in a hundred trillion of a pixel. And it has one free parameter that the recipe never names, which is the distance from the eye to the panel.

construction · alberti
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
00.50011.50205101520the dome's centre, off the entrance pupil (mm)worst departure from the pinhole it would be in air (degrees)centred: exactly zero6 mm → 0.635°a 100 mm dome in acrylic, n = 1.4910.106° per mm of centring error

The port that is not there

A flat window into water costs a lens a third of its field. A sphere centred on the entrance pupil costs nothing at all — not nearly nothing, exactly nothing — and six millimetres off centre costs 0.635°.

refraction · port

Named alongside it

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

Vanishing pointCritical angleFocal lengthRefractive indexAngular diameterApparent depthArea lightbraccioCamera calibrationCausticcentre of projectionCentric point

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