The standard semiclassical approximations in scattering theory break down in four well-known situations, that correspond to some of the most interesting scattering effects. In order to treat them, one must be able to handle diffraction, a notoriously difficult subject involving the dynamical aspects of wave propagation.

The basic theme of this book is how to deal with these critical effects. Fortunately for the theorist, there exists an exactly soluble model that exhibits all of them, the scattering of light by a homogeneous spherical particle. Some of the most beautiful phenomena in nature, coronae, rainbows and glories, are visual manifestations of the critical effects contained within this model. The model is not only soluble: it describes with extremely high accuracy the actual behavior of small liquid droplets.

The formally exact solution of the light scattering problem, obtained by Mie at the beginning of this century (and even earlier by Lorenz), is in the form of an infinite series, the well-known partial-wave series; analogous problems for elastic waves had been solved in this form several decades before. During this period spanning over a century, many important contributions to mathematical physics, particularly in connection with special functions and asymptotic approximation methods, originated in the treatment of these problems.

Unfortunately, the series converges very slowly under semiclassical conditions. In view of the manifold practical applications, substantial effort has been devoted to developing fast computer programs for the numerical summation of the series solution.