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Snell’s law, proved by Willebrord Snellius states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of the indicies of refraction.
nisin(ϴi) = nrsin(ϴr)

Drag around the circle (or double-click anywhere) to change the angle of the incident ray, and watch how the refracted ray reacts.

Change the indicies of refraction with the sliders, number input boxes, or drop-down menus. Five “unknown” values are included—substitute the known values into Snell’s law to find them!

ni:
ϴi:
nr:
ϴr: