A generalization of Snell's law
Hawkins, Michael L.
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This thesis presents several derivations of Snell's Law of Refraction and one of the principle of reflection. In all of these, we place different constraints upon the problem and produce the familiar laws governing reflection and refraction. The main result of this research is the expression found for Snell's Law of Refraction in which the velocity of the light particles in the medium depends upon direction. We also use inverse problems to find the index of refraction needed to move along any desired family of curves. Finally, we derive a general expression that generates a family of curves given any index of refraction. This research has several applications in the area of acoustical and optical wave propagation. In the area of acoustics, the inverse problems enable us to predict the path followed by sound waves for a given medium. This would allow for military use in the area prosecuting submarine contacts and in ocean bottom surveys. The inverse problems also have applications to the bending of light rays used in laser technology. Although this paper derives several generalizations of Snell's Law of Refraction there are still areas that require further research.
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