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Chapter 1:
Law of Refraction: The Foundation of Geometrical Optics
Author(s): Max J. Riedl
Published: 2009
DOI: 10.1117/3.835815.ch1
1.1 Introduction Snell's law of refraction is the fundamental law that governs geometrical optics. We begin, therefore, with the proof of this basic rule, as it has been verified by Fermat. We then demonstrate how this surprisingly simple law can be applied to graphical ray tracing. With the equations for paraxial ray tracing, we provide the tool required for the initial optical design phase. These equations are sufficient to determine the third-order aberrations, which will be used throughout the book. 1.2 Fermat's Principle 1.2.1 Historic remarks Pierre de Fermat was a jurist and mathematician. He pursued his mathematical avocation mostly for his own enjoyment. He formulated his famous theorem in 1657. It declares that light takes the path that requires the least time. His reasoning led to the proof of the law of refraction, which Wilibrord Snel van Royen found experimentally some 20 years earlier. This law of refraction is the foundation of geometrical optics and is stated by n′sini′=nsini, where n and n′ are the indices of refraction of the media before and after refraction. The angle of incidence is i, and the angle of the ray is i′, relative to the normal, after refraction.
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Geometrical optics

Ray tracing

Aspheric lenses

Light emitting diodes

Monochromatic aberrations

Optical design

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