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 with this problem?

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.

 

[HallsofIvy]

I can't imagine what this has to do with differential equations!

 

[DrPhil]

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

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.

For us to solve this as a math (trigonometry) problem, you have to tell us ALL of the physics that is going on, and what equations you have to work with. Please define what "o" and "e" waves are. What is the significance of the optic axis? How does the D vector change when you cross a surface?

I surmise that the incident light is unpolarized, so intensities in the o and e (directions??) are equal. The D vector is random. Is there some value of the angle of incidence that results in one polarization being reflected and the other refracted? The physics here seems more significant than the algebra.