# Intensity of p-polarized light through stack of plates

• sergiokapone
In summary: This introduces some complexities into the equations that might not be immediately apparent. ##In summary, the intensity Fresnel equations for reflected p-polarized light are $$\label{a}\frac{I_{p_{refl}}}{I_{0p}}=\frac {\tan^{2}(i-r)}{{\tan^{2}(i+r)}}$$and for refracted one is\label{b}\frac{I_{p_{refr}}}{I_{0p}}=1 - \frac {\tan^{2}(i-r)}{{\tan
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.

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.

Last edited:

## 1. What is the definition of p-polarized light?

P-polarized light refers to light that is polarized in the plane of incidence, meaning the electric field vector is perpendicular to the plane of incidence.

## 2. How is the intensity of p-polarized light measured?

The intensity of p-polarized light can be measured using a polarimeter, which measures the angle of polarization of the light. It can also be calculated using the Malus' Law equation, which relates the intensity of polarized light to the angle of polarization.

## 3. What factors affect the intensity of p-polarized light through a stack of plates?

The intensity of p-polarized light through a stack of plates is affected by the number of plates, the angle of incidence, the thickness of the plates, and the refractive index of the plates.

## 4. How does the intensity of p-polarized light change as it passes through a stack of plates?

The intensity of p-polarized light decreases as it passes through a stack of plates due to the phenomenon of multiple reflections and interference. This causes some of the light to be reflected and some to be transmitted, resulting in a decrease in overall intensity.

## 5. Why is it important to understand the intensity of p-polarized light through a stack of plates?

Understanding the intensity of p-polarized light through a stack of plates is important in various fields, such as optics, materials science, and engineering. It can be used to design and optimize systems that utilize polarized light, such as polarizers, filters, and optical devices.

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