# Intensity conservation during refraction

1. Dec 8, 2013

### lakmus

Hi,
I try to solve excercises from the book Stellar Atmospheres by Mihallas. I'm stuck on this one:
By use of Snell's law,
$n_1(\nu)\sin{(\theta_1)}=n_2(\nu)\sin{(\theta_2)}$,
in the calculation of the energy passing through an unit area on the interface between two dispersive media with differing indices of refraction, show that
$I_{\nu}n_{\nu}^{-2}$
is a constant.

Well I tried at firts write just conservation of energy for intensity (here is the assumption that all light goes thru the interface). From definition of intensity and rewriting and solid angle by
$\mathrm{d}\omega=\frac{\mathrm{d}S \cos{\theta}}{r^2}$
I got:

$I_1 \cos^2{(\theta_1)} = I_2 \cos^2{(\theta_2)}$,
where index 1 is for light in the medium with refraction index $n_1$, index 2 analogically.
Using Snell's law does not helped to get right result.

So I tried calculate some reflection, but I could not get the right result like Mihallas - $I_{\nu}n_{\nu}^{-2}$ .

It's the firt exercise in the whole book, so I supose it should be easy, bud I can't find out, where I'm wrong.