Calculating Polarization by Reflection

All we need to solve these problems are the indices of refraction. Air has $n_1=\mathrm{1.00,}$ water has $n_2=1\text{.}\text{333,}$ and crown glass has ${n\prime }_2=1.520$. The equation $\text{tan}{\theta }_{\text{b}}=\frac{n_2}{n_1}$ can be directly applied to find ${\theta }_{\text{b}}$ in each case.

Putting the known quantities into the equation

gives

Solving for the angle ${\theta }_{\text{b}}$ yields

Similarly, for crown glass and air,

Thus,

Light reflected at these angles could be completely blocked by a good polarizing filter held with its axis vertical. Brewster’s angle for water and air are similar to those for glass and air, so that sunglasses are equally effective for light reflected from either water or glass under similar circumstances. Light not reflected is refracted into these media. So at an incident angle equal to Brewster’s angle, the refracted light will be slightly polarized vertically. It will not be completely polarized vertically, because only a small fraction of the incident light is reflected, and so a significant amount of horizontally polarized light is refracted.