Incident Angle Limitation Derivation in Optical Fibre

1. The problem statement, all variables and given/known data
derive the angle of limitation sinθ=[(n2^2-n3^2)^1/2]/n1

n1 is the air out side of the fibre
n2 is inside of the fibre
n3 is the fibre wall

2. Relevant equations

Snells Law:


3. The attempt at a solution

I’m pretty stuck and don’t really know where to go after getting the angles from geometry. I have pi/2-θ2 for the angle of reflection off of the optical wall. So I put this angle into Snells Law then just kind of get stuck.

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