Mapping diamond surfaces using interference

This page represents a ongoing project dealing with using interference patterns to map the surface of a diamond wafer. Since this is my first page, you'll have to excuse any blatant errors that I do not pick up on immediately. Currently this page will represent my work with Dr. Richard Jones on an approximation to the beam splitter featured in the Michelson interferometer. I will start by giving a brief introduction to electromagnetic radiation, then move on to the approximation itself (including graphs,etc.).

A Bit on Electromagnetic Radiation

Using Maxwell's equations we can find solutions for a travelling wave comprised of two perpindicular oscillating electric and magnetic fields, whose direction can be giving by the Poynting vector.

Maxwell's Equations

But, what if I need to make formulas? ${\frac {1}{\sqrt {2\pi \sigma ^{2}}}}e^{-{\frac {1}{2}}{\frac {(x-x_{0})^{2}}{\sigma ^{2}}}}$ I have no idea what that will look like, but let's try it. We can also do vector equations, such as Gauss's Law

${\vec {\nabla }}\times {\vec {D}}={\frac {\rho _{ext}}{\epsilon _{0}}}$

(1)

Next let's make some chapter headings.

Chapter 1

Chapter 2

Chapter 3

Chapter 4