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

Sensor format — where it appears

The rectangle of silicon behind a lens, whose width turns a focal length into an angle and without which it is not one. It is why a focal length in millimetres means nothing on its own, and why the same lens is a wide angle on one camera and a portrait lens on another.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

full frame · 39.6°APS-C · 26.6°Micro Four Thirds · 19.6°1 inch · 15.0°phone (1/1.7″) · 8.7°one 50 mm lens · the angle is a property of the rectangle behind itMicro Four Thirds: 2.00× diagonal, 2.08× wide, 1.85× tall50 mm across five formats39.6° down to 8.7°

A focal length is not an angle

Fifty millimetres means nothing until a rectangle is named behind it. The same lens is 39.6° across full frame, 26.6° across APS-C and 8.7° across a phone sensor — and the distance the resulting print is correct from depends on the ratio of the two, so two cameras matched on angle agree exactly whatever their formats.

sensor · Format 50 mm on full frame · 39.6° acrossphone3.71×94 mm correctlaptop1.28×431 mm correct27-inch monitor0.78×829 mm correcttelevision1.52×1.7 m correctcinema0.84×16.7 m correct×1 — standing at the station pointhow many times further away the reader is than the picture's own station pointworst is the phone at 3.71×

The screen sets the distance

Every viewing distance quoted for a picture on a page is conditional on an assumed figure width. Replace the assumption with an actual chain — focal length, sensor width, display width — and the same 50 mm frame is correct from 9 cm on a phone, 83 cm on a monitor and 16.7 m in a cinema. Nobody is standing at any of them.

screen · Station 34363840-0.50000.5001distance the lens is focused at (m, log scale)horizontal angle of view (degrees)38.99 at 3 m37.76 at 1 m35.90 at 0.5 m39.60° at infinity35.90° at 0.5 m

Focusing is a zoom

A 50 mm lens focused at half a metre is not a 50 mm camera. It stands 55.56 mm from the sensor, its picture is a pinhole picture at that distance, and it covers 35.9° where the same lens at infinity covers 39.6°. Recover the camera from the picture and it reports 55.56 mm. Read the picture with the engraved 50 mm instead and a right angle comes back as 96.0°.

sensor · Format

Named alongside it

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

field of viewFocal lengthStation pointViewing distanceDemonstrationPicture planeSubtended angleAspect ratioCamera calibrationCrop factorDepth compressionPrincipal point

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