Question

for a beam of light in air (n = 1.0) that becomes polarized off of an unknown material with a brewsters angle of 57 degrees, what is the index of refraction for the unknown material?

0.75
1.1
1.53
1.33
cannot be determined

Explanation:

Step1: Recall Brewster's law

Brewster's law is given by \( n = \tan\theta_B\), where \(n\) is the refractive index of the second medium (unknown material), \(\theta_B\) is the Brewster's angle.

Step2: Substitute the given value

We are given \(\theta_B = 57^{\circ}\), so \(n=\tan(57^{\circ})\).
Using a calculator, \(\tan(57^{\circ})\approx1.54\) (close to \(1.53\) considering possible rounding differences in calculator settings or problem - level approximations).

Answer:

1.53