# Homework Help: Solving index of refraction for Total Internal Reflection

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1. Mar 18, 2015

### RaulTheUCSCSlug

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

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

lambda_n=lambda_n

3. 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.

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.

2. Mar 18, 2015

### ehild

3. Mar 18, 2015

### RaulTheUCSCSlug

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.

4. Mar 18, 2015

### ehild

Find the angle of incidence at S2.

5. Mar 18, 2015

### 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?

6. Mar 19, 2015

### ehild

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.