Calculate the critical angle for the prism described above S

Calculate the critical angle for the prism described above.

Solution

from the snell\'s law : sin(x)*n₁ = sin(y)*n₂

where x is angle of incidence, y is angle of refraction

n₁ is refractive index of medium 1 and n₂ is refractive index of medium 2

here y has to be 90 degrees for TIR to take place, and then x becomes critical angle

so sin(x) = n₂/n₁

so x = sin^-1(n₂/n₁) = theta_c