Question

If the critical angle for light at an interface between certain substances is 54.2 degrees, what is the polarizing angle at this same interface?

I am confused!

Answer 1

Use the critical angle to get the index of refraction ratio, N1/N2

Sin 54.2 = N2/N1 = 0.81106
N1/N2 = 1.233

For the polarizing (Brewster) angle, A

tan A = N2/N1

N2/N1 = 50.1 degrees

See http://en.wikipedia.org/wiki/Brewster's_angle
for detailed explanation

Answer 2

my book says the answer is 39 degrees..

Answer 3

Right.
arctan N2/N1 = arctan 0.81106 = 39.0 degrees

I failed to use the formula correctly