Series

Mirror — the series

4 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. grey: the reflectiontwo routes, agreeing to 0e+0 px after one flip

    A mirror is a second camera

    Reflect the scene and photograph it, or reflect the camera and photograph the scene. The two routes disagree by 315 px and agree to the last bit once one axis of the image is reversed — which is the whole of why a mirror is said to swap left and right, written down.

    part 3 · light
  2. horizoncorrect from 20 cm, at 160 mm wide44° across

    Measured down from the waterline

    Whatever stands so far above the water, draw its reflection the same distance below. Through a vertical picture plane that is not an approximation — it is the reflection, to the arithmetic floor. Tilt the camera twenty-two degrees and it is eleven pixels out. Draw a gull, which touches the water nowhere, and guessing its waterline point wrong by two metres of depth costs fifty.

    part 4 · wrong
  3. correct from 15 cm, at 160 mm widereflecting and refracting · 6.0e-12 px

    One surface, two images

    A water surface reflects what is above it and refracts what is below it in the same photograph, from the same plane. The reflected half has a centre of projection to 1 × 10⁻¹⁴ m and every theorem about central projection applies to it; the refracted half misses its own best-fitting point by 28.6 mm and none of it does. And the landscape manual's rule for drawing a reflection turns out to be the epipole placed at infinity, which is why it costs nothing at zero tilt and 11.5 px at twenty-two degrees.

    part 5 · refraction
  4. the reflected eyecorrect from 16 cm, at 160 mm widetaught rule 1.26 m out

    A mirror that is not parallel to the wall

    Carry the depth in front of the glass an equal depth behind it, square to the wall. That is exact for a mirror hung parallel to the wall and 1.26 metres — 107 pixels — out for one turned 20°. Two invariants survive the turn instead, and one of the two nearly did not survive being tested, because it had been written in a form that could not fail.

    part 5 · wrong

All series