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Re: Snell (in Calcite)

Thanks Mojca:

Can you give me a reference which clearly states that
Snell's law to E rays is valid for uniaxial crystals?
In the last several days I was collecting data whose
interpretation is based on the assumption that Snell's
law is valid. The reference would allow me to skip
the experimental verification, it is not easy unless
one has a goniometer.

The conclusions are so excting but untill I have more
confidence I prefer not to say anything else at this
stage. By the way, your message, of sevaral weeks
ago was partially responsible for the undertaking of
the experiment. (I do not have Born's textbook near
by but I will certainly look into it when I can).

Mojca Cepic wrote:

Snells law is still valid but the refraction index for the
parallel polarization is angle dependent i.e.

Sin[t1]/Sin[t2] = n(t2)

For uniaxial crystals the mathematics is easy for a case where
optical axes is perpendicular to the surface or with minor
changes is parallel to (Born and Born, Optics). The wave
velocity in t2 direction in the crystal is
v(t2) = c^2/no Cos[t2]^2 + c^2/ne Sin[t2]^2

where c is the speed of light, t2 is the refracting angle, no is ordinary
refractive index and ne is extraordinary refractive index. Both equations
have to be solved selfconsistently.

It has to be mentioned, that the equation is valid for the E wave normal.
The ray has a different direction inside the crystal. And E wave normal
is not perpendicular to the ray.

Regards Mojca Èepiè

Dr. Mojca Èepiè or Doc. Dr.
Mojca Èepiè
Jo*ef Stefan Institute Faculty
of Education
Jamova 39
Kardeljeva pl. 16
1000 Ljubljana 1000
Ljubljana
Slovenia
Slovenia
e-mail: mojca.cepic@ijs.si
tel.: +386 61 17 73 471 +386 61 18
92 200
fax.: +386 61 17 73 716 +386 61 18
92 233