Solving index of refraction for Total Internal Reflection

[RaulTheUCSCSlug]

Homework Statement

Homework Equations

Snell's Law
n₁sin(theta_1)=n₂sin(theta_2)
Total Internal Refraction:
sin(theta_c)=(n_2/n_1)

lambda_n=lambda_n

The Attempt at a Solution

So I drew the triangle and this is what I got, and well here is just a picture so far of what I have.

[/B]

I've done this problem before and got n=(theta)-(arcsin((sin(theta)/n)) and from there I have no idea. But I did a different approach. Any ideas. I've tried differentiating implicitly after that and trying to integrate and just got a huge mess.

 

[ehild]

Show your work in readable form.

 

[RaulTheUCSCSlug]

Show your work in readable form.

I just wrote down what I know and some equations, I found out the angle of refraction when the laser beam first enters. But I don't know what to do after.

 

[ehild]

Find the angle of incidence at S2.

 

[RaulTheUCSCSlug]

It would be 90 degrees minus the angle of refraction. But doesn't it have to equal the angle at which it internally reflects?

 

[ehild]

It would be 90 degrees minus the angle of refraction. But doesn't it have to equal the angle at which it internally reflects?

Yes, it should be equal or greater than the critical angle, at which internal reflection occurs. But it is not 90°minus the angle of refraction at S1. Give it in terms of theta and the angle of refraction.