Angle of refraction, Refractive Indices, and D Vectors

[Joystar77]

I have no idea how to do this or where to start. Can someone please help me?

At the He-Ne laser wavelength (L= 632.8 nm) the refractive indices of crystal quartz are n o = 1.54264 and n e = 1.55171 calculated from its Sellmeier equation. The laser is incident from the air onto the surface of crystal quartz at an angle of incidence of 45 degrees. For each of the following three cases, please find the angle of refraction, find the refractive indices, and briefly describe the direction of the D vectors for the o- and e- waves inside the crystal.

a.) The optic axis is parallel to the plane of incidence, and is also parallel to the surface of the crystal.

b.) The optic axis is perpendicular to the surface of the crystal.

c.) The optic axis is perpendicular to the plane of incidence.

 

[Aaron Bex]

Answer:

a.) The angle of refraction is approximately 22.3 degrees, the refractive indices are n o = 1.54264 and n e = 1.55171, and the direction of the D vectors for the o- and e- waves inside the crystal will be parallel to the optic axis and parallel to the plane of incidence.

b.) The angle of refraction is approximately 35.3 degrees, the refractive indices are n o = 1.54264 and n e = 1.55171, and the direction of the D vectors for the o- and e- waves inside the crystal will be perpendicular to the optic axis and perpendicular to the surface of the crystal.

c.) The angle of refraction is approximately 19.7 degrees, the refractive indices are n o = 1.54264 and n e = 1.55171, and the direction of the D vectors for the o- and e- waves inside the crystal will be perpendicular to the optic axis and perpendicular to the plane of incidence.