Reflection and Refraction on a Flat Surface between Two Different Materials

When a ray of light hits the surface between two different materials, part of it is reflected and part of it is refracted through the second material. Call (Subscript[α, i]) the angle between the incoming ray and the normal to the surface. The angle of reflection is (Subscript[α, i]), while the angle of refraction is (Subscript[α, r]), satisfying (Subscript[n, 1])sin((Subscript[α, i]))=(Subscript[n, 2])sin((Subscript[α, r])), where (Subscript[n, 1]) and (Subscript[n, 2]) are the ratios between the speed of light in a vacuum and in the materials, (Subscript[n, 1])=c/(Subscript[v, 1]) and (Subscript[n, 2])=c/(Subscript[v, 2]). There is no reflected ray when (Subscript[n, 1])=(Subscript[n, 2]).

If the angle (Subscript[α, r]) is greater than 90°, there is total reflection, which means that the ray does not cross the surface. (This is explicitly indicated in the panel on the right as "(Subscript[α, r]) does not exist".)

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Contributed by: Stra Federico

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