# Total Internal Reflection

1. Apr 17, 2012

### ParoXsitiC

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

Find the lowest angle of θ1 given the apex angle is 60°. Air (n=1) is on the outside and inside (n=1.5)

ϕ is defined as 60 degrees.

2. Relevant equations

3. The attempt at a solution

θc = sin-1($\frac{1.00}{1.50}$) = 41.81°

To my understanding, θ1 must angle in such a way to make r (the angle of refraction) to be equal to the critical angle. At this point you will start having TIR.

They state that r = ϕ + θc
How? I am not seeing it.

Once I found r, I can just use snells law to find θ1 - but I don't understand how to find r.

Last edited: Apr 18, 2012
2. Apr 18, 2012

### PeterO

Need some sort of diagram so the position of this θ1 is knows.

Last edited by a moderator: May 5, 2017
3. Apr 18, 2012

### ParoXsitiC

I give one but perhaps its not showing for you since its minus.com, here it is on imgur

4. Apr 18, 2012

### PeterO

Image came through that time.

If you look at the top triangle - the one with the 60o angle, the other two angles are (90 - r)o and (90 - θc)o

That means [(90-r) + ϕ + (90-θc)] = 180

so 180 -r + ϕ - θc = 180

or -r + ϕ - θc = 0 which means r = ϕ - θc

Notice that is slightly different to what was in your original solution. I suspect something was wrong.