# I Intensity of p-polarized light through stack of plates

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1. Apr 18, 2017

### sergiokapone

As one know, the intensity Fresnel equations
for the reflected p-polarized light
\label{a}
\frac{I_{p_{refl}}}{I_{0p}}=\frac {\tan^{2}(i-r)}{{\tan^{2}(i+r)}}

and for the refracted one is

\label{b}
\frac{I_{p_{refr}}}{I_{0p}}=1 - \frac {\tan^{2}(i-r)}{{\tan^{2}(i+r)}}

where $i$ - angle of incidence, $r$ - angle of refraction, $I_{op}$ -intensity of incident p-polarized light.

Suppose, we sent p-polarized light to a stack of plates (10 plates with $n = 1.5$).
I expected the intensity of reflected p-polarized light subject to equation (1) and also the intensity of p-polarized light passed across stack of plates subject to equation (2) with some downgrading due to absorption.

I get an experimental data in picture:

%====================================
\begin{filecontents}{plate.dat}
angle refracted reflected
7 8 10
5.5 8 20
6 7 30
11 3.5 40
11.5 2 45
12 1 50
12 0.6 52
10.5 0 56
8.3 1 60
3 3 65
\end{filecontents}

The best fit reflected p-polarized light (blue line) is

\label{fita}
\frac{I_{p_{refl}}}{250}=\frac {\tan^{2}(i-r)}{{\tan^{2}(i+r)}}

It seems reasonable.
But fit with equatuion (2) looks bad (red line) :
\label{fitb}
\frac{I_{p_{refr}}}{1/n\cdot 250}=1 - \frac {\tan^{2}(i-r)}{{\tan^{2}(i+r)}}

I have no idea how to explain it.

2. Apr 19, 2017

Multiple reflections are somewhat difficult to take into account using these equations, but the transmitted intensity for 10 plates should be approximately $\tau_{ten}=\tau_{single}^{10}$.(This equation is only a rough approximation and doesn't take the transmission from multiple reflections into account.) From looking at your data, I don't think absorption losses account for a tremendously high percentage. Instead, the transmission through the 10 plates at and near the Brewster angle appears to be quite high (near 100%), but I think you normalized the intensity rather than displaying absolute transmittance. $\\$ Editing: I would also suggest you check the equations and how they might apply. The Fresnel equations are normally for a single dielectric interface. If you have 10 plates, that could be as many as 20 air/material dielectric interfaces, rather than 10.