Critical angle — where it appears
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.
The sky inside a cone
From under water the whole sky — every direction out to the horizon — arrives inside a cone of 48.61°. Outside it the surface is a mirror. That cone is a picture surface, and it has a distortion no surface in the curved field has — an area scale that runs to zero.
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°.
Named alongside it
The objects these essays reach for when they reach for this one.
PinholeAnisotropyApparent depthArea scaleConformalDome portEntrance pupilfield of viewFlat portHorizonNormal incidenceParallax