Plane of incidence — where it appears
Named by 5 essays across one field — each of them below, with the objects they name alongside it.
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.
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.
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.
A straight stick tests the index only across the sight
Told that each stick is straight, three eyes fitting a water surface's height and its index still slide down the valley between them — when the stick leans away from them. A wrong index carries such a stick into another straight stick, off its line by 0.016 mm and 116 mm short. Turned to lean across the line of sight, the same wrong index bows it by 2.2 mm, and the straight-line fit's slide falls from 0.058 to nothing. A tape on the stick, read only to ±50 mm, stops the slide outright.
A bowed stick is read as a wrong index
Holding a stick to a straight line cured the slide in a refraction fit — but only for a stick leaning across the sight, where a wrong index bows the read stick by two millimetres. A stick that is itself bowed by a millimetre in the same plane is, to that constraint, a straight stick seen through the wrong index: read without error, it moves the fitted index by 0.074 one way or 0.062 the other, and at a quarter pixel the constraint's bias overtakes the slide it was removing at about three-quarters of a millimetre of bow. Its misfit is a fiftieth of a pixel, so nothing in the residuals says so. A tape, which measures length, does not notice the bow at all.
Named alongside it
The objects these essays reach for when they reach for this one.
Refractive indexTriangulationApparent-depthCollinearityRefractionSnell's lawAstigmatismBiasleast squaresBaselineCalibrationcentre of projection