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In Chapter 1 the concept of rays was introduced. When the ratio of wavelength to aperture dimension approaches zero, diffraction effects can be neglected as justified by the Eikonal equation, and electromagnetic waves can be treated as rays propagating in directions perpendicular to locations of constant phase, known as wavefronts. In this chapter, the concept of electromagnetic (EM) rays is developed further to explain image formation. Central to image formation is the concept of the optical path, which determines which paths may be taken by a given ray. These requirements are described be Fermat's principle. The curvature of lens and mirror surfaces optimal to image formation are derived from consideration of Fermat's principle. After developing condition required for image formation by a single lens (or mirror), combinations of lenses are considered. The approach is that of system engineering, where the output of a given lens is the input to the following one. Here, output represents the image and input represents the object. After developing the theoretical requirements for image formation, the selfoc optical fibers, developed in Chapter 1, are shown to be completely analogous to ordinary lenses. Both satisfy these requirements. Matrix optics are shown to be a useful tool for multielement optical system design.
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