I have been studying the relation between Brewster's angle and the critical angle, and I am left with the following question:
\begin{align}
\tanθ_p & =\frac{1}{\sinθ_c} \\
\tanθ_p & =\frac{n_1}{n_2} \\
\sinθ_c & =\frac{n_2}{n_1},
\end{align}
where $n_1$ has to be greater than $n_2$.
For the critical angle, $n_1$ has to be greater $n_2$. Is there a similar rule for Brewster's angle as well: Does $n_1$ also have to be greater than $n_2$?
In other words, does the polarisation of light by reflection only happen when the wave is travelling in a less dense medium and hits a denser medium? Or can the polarisation of light by reflection happen when a wave is travelling in a denser medium and hits a less dense medium as well?
Best Answer
The Brewster angle $\theta_B$ is defined by $$ \tan(\theta_B) = \frac{n_2}{n_1}. $$ Since the range of the tangent function over $\theta_B\in(0,\pi/2)$ covers all positive real numbers $(0,\infty)$, there will always be a Brewster's angle, where $p$-polarized light is not reflected, regardless of the combination of media. The only conclusion that you can draw from the fact that $n_2>n_1$ (resp. that $n_1>n_2$) is that you will have $\theta_B> 45°$ (resp. $\theta_B < 45°$).