# Solving simultaneous equations

## Homework Statement

A uniaxial crystal of indices n0 and ne is cut so that the optic axis is
perpendicular to the surface. Show that for light from the outside at
an angle of incidence θi, the angle of refraction of the e-ray is

## The Attempt at a Solution

I solved for ne by dividing both sides of the third equation by what appears to be an ellipse equation and taking the square root of both sides, then plugging it in into Snell's law (the second equation). It's become ugly and confusing, though. Help is appreciated.

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## Homework Statement

A uniaxial crystal of indices n0 and ne is cut so that the optic axis is
perpendicular to the surface. Show that for light from the outside at
an angle of incidence θi, the angle of refraction of the e-ray is

## The Attempt at a Solution

I solved for ne by dividing both sides of the third equation by what appears to be an ellipse equation and taking the square root of both sides, then plugging it in into Snell's law (the second equation). It's become ugly and confusing, though. Help is appreciated.
What is θ, that you have in your 2nd and 3rd equations (along with θi and θe)?

Your first equation should be using the lower-case forms of θi and θe, rather than the upper-case forms (##\Theta_i## and ##\Theta_e##). That could be confusing to some.

Sorry about that... I screenshotted it straight from our PDF textbook. I believe θ = θe.

I solved it, thanks anyway.