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Full Description
Several optical phenomena can occur when the sun is near the horizon, some of which can actually be seen, for instance as a dark strip in the middle of the solar disk, or as a green flash. These are a result of the way the atmosphere affects the geometry of light rays. In this book, Broer uses the Fermat principle to deduce laws for refraction and reflection. By expressing these as conservation laws, he can handle both the case of inhomogeneous layers of air and the case of continuous variation in the refraction index. Building from this elementary theory, more advanced mathematical theories are discussed, including how the Fermat Principle leads to a Riemannian metric whose geodesics are the paths of light rays, thus demonstrating the physical applicability of Riemannian geometry. Intended for teachers and professors to enlighten their courses, or for students and researchers in mathematics, science and engineering.
Contents
1. Introduction and overview; Part I. Geometry of Light Rays in the Atmosphere: 2. Geometric optics; 3. Atmospheric optics; 4. Light and the cycloid; Part II. Light Rays as Geodesics: 5. The principles of Fermat and Hamilton; 6. The brachistochrone revisited; 7. Light rays as geodesics on a surface of revolution; 8. Scholium generale.
