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.
Henk Broer completed his Ph.D. in mathematics and natural sciences at Rijksuniversiteit Groningen, The Netherlands, and has been professor of dynamical systems there since 1991. He was the scientific director of the Johann Bernoulli Institute for Mathematics and Computer Science, and is currently both the chairman of the section mathematics of KNAW and the editor-in-chief of the journal, Indagationes Mathematicae. He has held visiting positions at Boston University, the Universite de Bourgogne, France, the Universitat de Barcelona and Georgia Institute of Technology, and has co-initiated a number of national institutions in the Netherlands, including Mastermath and Platform Wiskunde Nederland.