Changes

== Huygen's Principle ==

== Huygen's Principle ==

Each point on the surface can be approximated by an outgoing spherical wave (away from the surface).  These waves have solutions such as <math>\boldsymbol{E} = \boldsymbol{E_0} e^{i \left( \boldsymbol{k \cdot x} - \omega t \right)}</math>

Each point on the surface can be approximated by an outgoing spherical wave. [[Image:huygensprinciple.gif|thumb|Huygen's Principle Illustrated (courtesy of http://www.mathpages.com/home/kmath242/kmath242.htm]] Depending on the nature of the surface topology, the shape will be contained in these outgoing spherical waves, but will diffuse over some distance. 

 

In our model of the diamond surface, Huygen's principle can be used to determine the forward distance from the surface when the reflected light will no longer contain a ''valid'' image of the surface.  Using the diagram at right, [[Image:ResDiagram1.jpg|thumb|Surface Schematic]] and some knowledge of the experimental setup, a rought estimate for the forward distance ''L'' can be calculated using a small angle approximation for the angle.

 

<math>\boldsymbol{E} = \boldsymbol{E_0} e^{i \left( \boldsymbol{k \cdot x} - \omega t \right)}</math>

<math>\boldsymbol{E} = \boldsymbol{E_0} e^{i \left( \boldsymbol{k \cdot x} - \omega t \right)}</math>