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\author{Andrew Mark Allen}
\title{Physical Optics}
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\section{Light as a Wave}
Light is a wave :3

Ampere's Law: $\displaystyle{\oint{B \cdot dl  = \mu\left[I + \epsilon\frac{d(E\cdot A)}{dt}\right] }}$

 Faraday's Law: $\displaystyle{\oint{E \cdot dl  = -\frac{d(B\cdot A)}{dt} }}$

An electromagnetic wave that obeys Faraday's and Ampere's law must have:
\begin{enumerate}
\item
A magnetic field component related to it by $E=cB$
\item
A velocity of $c = \displaystyle{\frac{1}{\sqrt{\epsilon\mu}}}$
\end{enumerate}
Proof:

\todo{Rewrite her proof to show that E=cB}

\section{Wave Motion}
Given the basic requirement that $\psi = \psi(x,t) = \psi(x') = \psi(x \pm vt)$ where $x' = x \pm vt$, we can derive the general differential wave equation, $\displaystyle{\frac{\partial^2\psi}{\partial x^2} = \frac{1}{v^2}\frac{\partial^2\psi}{\partial t^2}}$

Note that while this equation applies to any wave, not all solutions to the equation are waves.

\todo{Write proof, rewrite section}

\section{Harmonic Waves}

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