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

total internal reflection — where it appears

The return of all the light striking a surface from the denser side at more than the critical angle, where refraction has no outgoing ray left to give. It is why a swimmer sees a bright disc overhead and a mirror beyond it, and why the disc's edge is sharp for geometry and soft for brightness.

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

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 the critical angle, 48.61°00.2500.5000.75010204060angle off the zenith (°)brightness, as the disc draws itfrom the zenith out to 60°bottom of albedo 0.3

The horizon is in the window and almost unlit

Snell's window holds the whole sky in a cone, right down to the horizon. Geometry says so and it is true. The surface passes less and less of that light towards the rim, so the last five degrees of sky get a quarter of a degree of the disc at under a third of their brightness. The window's famous edge, which looks like the surface's doing, depends on what is on the bottom, and over a white pool it disappears.

refraction · Snellwindow

Named alongside it

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

Area scaleCritical angleHorizonPicture surfaceAnisotropyConformalinstrument limit

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