Question

The absolute index of refraction for a substance in 2.0 for light having a wavelength of 5.9 x 10^-7 meter. In this substance, what is the critical angle for light incident on a boundary with air?

Answer 1

refractive index of air is (Wikipedia) n=1,000293
Snell's law gives (Wikipedia):
n1. sin theta1 = n2. sin theta2
Brewster's angle, or the critical angle is the angle where the theta of least dense material (here air) is 90 degrees:
\[\theta _{critical} = \sin^{-1} (n _{1} / n _{2} ) = \sin^{-1} (\frac{ 1,000293 }{2,0}) = 30^{0}\]