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. Bothe 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 Čepič
Dr. Mojca Čepič or Doc. Dr.
Mojca Čepič
Jožef 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