ABSTRACT

In a few simple configurations, analytical solutions are possible. They illuminate the problem and are useful for checking the correctness of a computer program. This chapter derives the efficiencies for small spheres of dielectric material. This is the basic section for understanding how and why interstellar dust absorbs and scatters light. A real grain is not a homogeneous continuum but a crystal built up from atoms, rather regularly spaced and separated by a distance, the lattice constant. Mie theory, which is based on the classical electrodynamics of a continuous medium, fails when the structure of matter or quantum effects become important. The chapter considers some quantum effects when discussing polycyclic aromatic hydrocarbons, a specific kind of very small carbon grains. It focuses on the influence of the surface in the case of small grains.