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Introduction to Geometric Optics

This SparkNote will apply what we have learned about scattering to the familiar concept of
reflection and the perhaps less familiar concept of refraction, the bending of light upon
transmission into a dielectric medium. We will see how the macroscopic laws of reflection and
refraction (Snell's Law) are a result of the interaction of many atomic and sub-microscopic
scatterers. In both cases, the laws can be derived directly from the boundary conditions implied
by Maxwell's equations. When considering refraction we will study the related phenomenon
of dispersion, exploring cases in which the amount of bending of a light ray is dependent upon its
frequency (or its wavelength). It is this effect which causes the splitting of white
light into a spectrum of colors (different wavelengths) by a prism. The notion of total internal
reflection (TIR), responsible for the transmission of light through optic fibers, will also be explored.
Finally, from Maxwell's equations we will deduce the so-called *Fresnel Equations,* which allow the relative
amplitude of reflected and refracted rays to be computed as a function of the angle from the normal to the interface.

In the last section we will examine a very practical aspect of optics by applying the laws of reflection
and refraction to geometrical optics proper. This analysis treats light as always propagating in straight
lines, ignoring the finite wavelength and thus neglecting any interference or
diffractive effects. Ray tracing for mirrors and lenses has immediate and obvious practical
applications in the design of microscopes, telescopes, and other optical instruments.