Following the rather lengthy mathematical onslaught in the theoretical development of scattering from a large dielectric sphere in the preceding chapter, it is perhaps time to take a break from these labors and apply the results to prediction of some measurable quantities. As well as judging the largesphere theory against the exact expressions provided by the Mie solution, some pleasure may also be found in using the results to explore various meteorological optical phenomena.

It cannot be emphasized too strongly that the preceding theory is exact, in the same sense that the Mie solution is exact. In principle we can calculate amplitudes and cross sections to all orders in β – it is not an approximate theory. In practice, however, one need only retain a few terms in the asymptotic expansions and in the residue series to achieve reasonable accuracy, so that we can appropriately approximate the theoretical expressions and reduce the calculational labor. However, this is also in contrast with the partial-wave expansions, which must include indices l to at least O(β). The difference between approximate theories and approximations to the exact theory is that in the latter we are able to control the estimates rather precisely. A separate issue relates to how many terms must be retained in the Debye expansion itself, and this will be addressed as the need arises.