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Snell (in Calcite)



Most of us are familiar with the first demo on birefringence.
Place a transparent calcite (parallel plate crystal) on a dot and
see two images, ordinary (O) and extraordinary (E). Turn
the crystal and see the E dot tracing a circle around the O dot.

Textbooks with which I am familiar say that O rays obey
Snell's law while E rays do not. But they do not describe
the law of refraction for E rays. For O rays the law of
refraction has two parts. (a) The refracted ray is in the
plane of incidence, (b) the angles are related by Snell's
formula, n1*sin(T1)=n2*sin(T2).

Textbooks say, and the demo illustrates, that (a) is not
satisfied by the refracted E rays. But what about (b)? The
angle T2 still depends on the angle T1. Does the Snell's
formula apply to E rays? If not then what is the relation
between T1 and T2? I am referring to angles with respect
to the normal at the point of incidence. Note that the
plane of incidence and the plane of refraction intersect
along the normal.
Ludwik Kowalski