
In accordance with Snell's law, μ=μDμR=sin90osinic
here ic is the angle of incidence.
μDμR=sinic
μ=μDμR=sinrsinA
=sin(90∘−A)sinA=cosAsinA
μDμR=tanA.
The critical angle is related to the angle A as tanA=sinθC
A=tan−1(sinθC).