Question

Because of an oil spill there is an oil sheen on the surface of the water in a lake. If the critical angle for a light ray leaving the water is 72degree, at what angle above the horizontal is the sun if sunlight reflected from the oily surface is completely polarized?

Answer 1

We need to find the Brewster angle first

$\tan\theta_b=\frac{n_2}{n_1}$

where $\theta_b,n_2,n_1$ is Brewster angle,index of refraction of denser medium,index of refraction of rarer medium

From Snell's law

$n_1\sin\theta_1=n_2\sin\theta_2$

At critical angle

$\theta_2=90^\circ$ and $\theta_1=72^\circ$

$\frac{n_2}{n_1}=0.95$

Putting in the expression for Brewster angle

$\tan\theta_b=0.95$

$\theta_b=43.56$

Angle above the horizontal where sun is

$90-43.56=46.44^\circ$