# Homework Help: Angle of refraction, Refractive Indices, and D Vectors

1. Nov 12, 2013

### Joystar77

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

OPL difference = triangle d n o

Phase difference = triangle does not equal 0 = k o triangle = 2 triangle/ x d (n o - n e)

3. The attempt at a solution

Sin Oi = n o sin 0 n e

O i = 45 degrees

Sin Oi = 1/ Square Root 2

Sin O no = 1 / 1.54264 Square Root 2

Sin O ne = 1 / 1.55171 Square Root 2

Triangle 0 = Sin + 1/ 1.54264 Square Root 2 - Sin + 1/ 1.55171 Square Root 2

Are any of these right for a, b, or c? If not, can somebody please explain step-by-step how to do these?