Concept

Critical angle — where it appears

3 essays name this object, across one field. 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
15°30°45°60°85°the rim: 48.61° from straight upbeyond it: the bottom, reflected45° of sky0.469460° of sky0.370275° of sky0.211485° of sky0.0738area scalen = 1.333, so the rim is at asin(1/n) = 48.61°area scale 0.563 at the centre, 0.0738 at 85°

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.

refraction · snellwindow
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.

PinholeAnisotropyApparent depthArea scaleConformalDome portEntrance pupilfield of viewFlat portHorizonNormal incidenceParallax

All concepts