Concept

Plane of incidence — where it appears

The plane containing an incoming ray and the normal to the surface it meets. Snell's law keeps the refracted and the reflected ray in that plane, which is why what a flat surface does to one ray can be drawn in a single section.

Named by 3 essays across one field — each of them below, with 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
eyethe sticktwo eyes side by sidea nodding headcorrect from 18 cm, at 160 mm widekink 14.96° · turn 4.29°

A straight stick in water is a kink and a curve

The bent stick is described as one kink at the surface. Traced point by point, the image two level eyes see leaves the surface 14.96° off a stick leaning 30° — the same whichever way it leans — and then keeps turning, by 1.11° when it leans away from the eye and 7.62° when it leans toward it. A photograph from the eye shows the kink and almost none of the curve, 1.63 px over 166 px, and when the stick leans straight toward or away from the eye it shows neither: the picture is one straight line.

refraction · Refraction
eyethe stickcorrect from 18 cm, at 160 mm widerays miss by 3.13 mm

The stick a stereo pair puts back

Two eyes side by side reconstruct a submerged stick exactly as the sagittal image — kinked 14.96° — and two eyes one above the other exactly as the tangential one, kinked 9.59°. Roll the baseline between them and the two rays to a point miss each other by up to 3.13 millimetres, past the 2.85 a pixel covers at that range, and the reconstruction is a third stick that is neither — 551 millimetres of a one-metre stick, with its tip at 0.405 metres against a true 0.866.

refraction · Refraction

Named alongside it

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

Apparent-depthSnell's lawAstigmatismRefractive indexTriangulationBaselinecentre of projectionCollinearityCritical angleMidpointPinholeRefraction

All concepts