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Update 2022-02-09 07:44

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Jean-Sébastien
2022-02-09 07:44:58 +01:00
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commit 3c40f5bfe8
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build/emdm_emwm_refl_oi.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-08 Tue 17:21 -->
<!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1616,7 +1616,7 @@ Table of contents
</ul>
</details>
</nav>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_emwm_refl_ni.html">Normal Incidence&emsp;<small>[emdm.emwm.refl.ni]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_refl_Fe.html">Fresnel's Equations&emsp;<small>[emdm.emwm.refl.Fe]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_refl.html">Reflection and Transmission&emsp;<small>[emdm.emwm.refl]</small></a></li></ul><div id="outline-container-emdm_emwm_refl_oi" class="outline-5">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emdm.html">Electromagnetodynamics in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm.html">Electromagnetic Waves in Matter</a></li><li><a class="breadcrumb-link"href="emdm_emwm_refl.html">Reflection and Transmission</a></li><li>Oblique Incidence</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_emwm_refl_ni.html">Normal Incidence&emsp;<small>[emdm.emwm.refl.ni]</small></a></li><li>Next:&nbsp;<a href="emdm_emwm_refl_Fe.html">Fresnel's Equations&emsp;<small>[emdm.emwm.refl.Fe]</small></a></li><li>Up:&nbsp;<a href="emdm_emwm_refl.html">Reflection and Transmission&emsp;<small>[emdm.emwm.refl]</small></a></li></ul><div id="outline-container-emdm_emwm_refl_oi" class="outline-5">
<h5 id="emdm_emwm_refl_oi">Oblique Incidence<a class="headline-permalink" href="./emdm_emwm_refl_oi.html#emdm_emwm_refl_oi"><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"/>
@@ -1660,7 +1660,7 @@ 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="orga1858e0">
<div class="core div" id="org699621d">
<p>
{\bf First law of reflection:}
the incident, reflected and transmitted wave vectors form a plane (called the plane of incidence) which also includes the normal to the surface.
@@ -1675,7 +1675,7 @@ Specializing (\ref{eq:RTObliquek}) to our notations, we have
with the incidence (\(\theta_I\)) and reflection (\(\theta_R\)) angles
and the angle of refraction (\(\theta_T\)) obey the following laws:
</p>
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<div class="core div" id="orgb0b59f9">
<p>
{\bf Law of reflection}
\[
@@ -1733,7 +1733,7 @@ while the third equation becomes
\]
Writing everything in terms of the incident amplitude, we get
</p>
<div class="main div" id="org4da7748">
<div class="main div" id="orgefa3e67">
<p>
{\bf Fresnel's equations for reflection and transmission amplitudes (parallel case)}
\[
@@ -1753,7 +1753,7 @@ Amplitudes for transmitted and reflected wave: depend on angle of incidence:
Behaviour: for \(\theta_I = 0\) we recover (\ref{Gr(9.82)}).
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>
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<div class="main div" id="orgd248cb3">
<p>
{\bf Brewster's angle {\it (at which the reflected wave amplitude vanishes)}}
\[
@@ -1788,10 +1788,21 @@ Of course, we get \(R + T = 1\) as expected.
<hr><div id="postamble" class="status">
<hr>
<div class="license">
<a rel="license noopener" href="https://creativecommons.org/licenses/by/4.0/"
target="_blank" class="m-2">
<img alt="Creative Commons License" style="border-width:0"
src="https://licensebuttons.net/l/by/4.0/80x15.png"/>
</a>
Except where otherwise noted, all content is licensed under a
<a rel="license noopener" href="https://creativecommons.org/licenses/by/4.0/"
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: 2022-02-08 Tue 17:21</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
<p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"></p>
</div>