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Update 2022-03-24 08:43

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Jean-Sébastien
2022-03-24 08:43:21 +01:00
parent 1d852e7213
commit 50704eba07
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build/emdm_emwm_refl_oi.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-03-22 Tue 10:52 -->
<!-- 2022-03-24 Thu 08:42 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
</summary>
<ul>
<li>
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
</li>
@@ -1635,14 +1635,14 @@ Transmitted wave:
\]
All waves have the same frequency \(\omega\). Since \(\omega = k v\), the three wavevectors are related by
</p>
<div class="eqlabel" id="orgd898837">
<div class="eqlabel" id="org512368e">
<p>
<a id="RTobliquek"></a><a href="./emdm_emwm_refl_oi.html#RTobliquek"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="orgabe9175">
<div class="alteqlabels" id="org1361b67">
</div>
@@ -1665,7 +1665,7 @@ These forms for incident, reflected and transmitted wave can be substituted in t
<p>
From now on we will orient the axes so that \({\boldsymbol k}_I\) lies in the \(xz\) plane. This means that \({\boldsymbol k}_R\) and \({\boldsymbol k}_T\) also lie in that plane. This is the
</p>
<div class="core div" id="org4e7e42a">
<div class="core div" id="org86dbe79">
<p>
<b>First law of reflection:</b>
the incident, reflected and transmitted wave vectors form a plane (called the plane of incidence) which also includes the normal to the surface.
@@ -1680,7 +1680,7 @@ Specializing <a href="./emdm_emwm_refl_oi.html#RTobliquek">RTobliquek</a> to our
with the incidence (\(\theta_I\)) and reflection (\(\theta_R\)) angles
and the angle of refraction (\(\theta_T\)) obey the following laws:
</p>
<div class="core div" id="org99d6843">
<div class="core div" id="orge55fc76">
<p>
<b>Law of reflection</b>
\[
@@ -1697,14 +1697,14 @@ and the angle of refraction (\(\theta_T\)) obey the following laws:
<p>
This takes care of the spatially-dependent exponential factors in the boundary conditions. The coefficients must further obey
</p>
<div class="eqlabel" id="orgdc0e7b2">
<div class="eqlabel" id="orga2e8f02">
<p>
<a id="EBRT"></a><a href="./emdm_emwm_refl_oi.html#EBRT"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="org6d39cd4">
<div class="alteqlabels" id="org12decff">
</div>
@@ -1750,18 +1750,18 @@ while the third equation becomes
\]
Writing everything in terms of the incident amplitude, we get
</p>
<div class="main div" id="org1929cd0">
<div class="main div" id="org29006a2">
<p>
<b>Fresnel's equations for reflection and transmission amplitudes (parallel case)</b>
</p>
<div class="eqlabel" id="org0b8be69">
<div class="eqlabel" id="orgd431e6b">
<p>
<a id="Fresnel"></a><a href="./emdm_emwm_refl_oi.html#Fresnel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="org617a8e4">
<div class="alteqlabels" id="orgd3db507">
</div>
@@ -1785,15 +1785,15 @@ Amplitudes for transmitted and reflected wave: depend on angle of incidence:
Behaviour: for \(\theta_I = 0\) we recover <a href="./emdm_emwm_refl_ni.html#ERT">ERT</a>.
For grazing waves \(\theta_I \rightarrow \pi/2\) we have that \(\alpha \rightarrow \infty\) and the wave is totally reflected. The most interesting angle is the one at which \(\alpha = \beta\) and the reflected wave has zero amplitude. This is known as
</p>
<div class="main div" id="org087c316">
<div class="eqlabel" id="orgb61a423">
<div class="main div" id="orgff8c46e">
<div class="eqlabel" id="org7aac922">
<p>
<a id="Brewster"></a><a href="./emdm_emwm_refl_oi.html#Brewster"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="org4e4ad5e">
<div class="alteqlabels" id="orgb13b73c">
</div>
@@ -1846,7 +1846,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
</div>
<div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-03-22 Tue 10:52</p>
<p class="date">Created: 2022-03-24 Thu 08:42</p>
<p class="validation"></p>
</div>