1
$\begingroup$

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?

$\endgroup$
1
$\begingroup$

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. $\theta_B < 45°$).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.