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Update 2022-02-09 22:41

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Jean-Sébastien
2022-02-09 22:41:42 +01:00
parent 3c40f5bfe8
commit f3c2446d19
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build/emdm_emwm_refl_oi.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-09 Wed 07:31 -->
<!-- 2022-02-09 Wed 22:40 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -408,17 +408,13 @@ Table of contents
<li>
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
</li>
<li>
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
</li>
<li>
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
</li>
<li>
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
</li>
<li>
@@ -430,29 +426,8 @@ Table of contents
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary>
<ul>
<li>
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
</li>
<li>
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
</li>
<li>
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
</li>
</ul>
</details>
</li>
<li>
@@ -1660,7 +1635,7 @@ 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="org699621d">
<div class="core div" id="orga0e77f3">
<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 +1650,7 @@ 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>
<div class="core div" id="orgb0b59f9">
<div class="core div" id="orgc1a2ec9">
<p>
{\bf Law of reflection}
\[
@@ -1733,7 +1708,7 @@ while the third equation becomes
\]
Writing everything in terms of the incident amplitude, we get
</p>
<div class="main div" id="orgefa3e67">
<div class="main div" id="org933ec71">
<p>
{\bf Fresnel's equations for reflection and transmission amplitudes (parallel case)}
\[
@@ -1753,7 +1728,7 @@ 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>
<div class="main div" id="orgd248cb3">
<div class="main div" id="orga399926">
<p>
{\bf Brewster's angle {\it (at which the reflected wave amplitude vanishes)}}
\[
@@ -1801,7 +1776,7 @@ 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: 2022-02-09 Wed 07:31</p>
<p class="date">Created: 2022-02-09 Wed 22:40</p>
<p class="validation"></p>
</div>