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== Huygen's Principle ==

== Huygen's Principle ==

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.

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 as the inverse of the distance traveled.  For nearly flat surfaces this diffusion will not be appreciable for a distance depending on the shape of the surface and plane wave solutions can be used to mirror reflected light.

 

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, an estimate for the forward distance ''L'' can be calculated using a small angle approximation for the angle.  Using the the diamond surface is about <math>5 \times 10^{-3} m</math> and the thickness is <math>5 \times 10^{-6} m</math>, the forward distance for image loss can then be deduced to be 5m.  Since this is much longer than the feature length.  Our experimental setup can be considered effective.

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, an estimate for the forward distance ''L'' can be calculated using a small angle approximation for the angle.  Using the the diamond surface is about <math>5 \times 10^{-3} m</math> and the thickness is <math>5 \times 10^{-6} m</math>, the forward distance for image loss can then be deduced to be 5m.  Since this is much longer than the feature length.  Our experimental setup can be considered effective.