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I Intensity of p-polarized light through stack of plates

  1. Apr 18, 2017 #1
    As one know, the intensity Fresnel equations
    for the reflected p-polarized light
    \begin{equation}\label{a}
    \frac{I_{p_{refl}}}{I_{0p}}=\frac {\tan^{2}(i-r)}{{\tan^{2}(i+r)}}
    \end{equation}

    and for the refracted one is

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

    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:
    989f09e890de2fd9ff83db9050b15ea6.png

    %====================================
    \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

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

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

    I have no idea how to explain it.
     
  2. jcsd
  3. Apr 19, 2017 #2

    Charles Link

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    Homework Helper

    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: Apr 19, 2017
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