54
K. D. Dahm and D. J. Dahm
It is straightforward to validate the equations presented throughout this section
for samples that are literally divided into distinct identical layers. For example, they
proved to work well for samples consisting of different numbers of identical plastic
sheets [15]. However, how can the concept of a “plane parallel layer” be meaningfully
applied to a particulate sample? The next section explores this question.
3.9 The Representative Layer
Previous sections have alluded to the mathematical approach of modeling a sample
as a series of identical plane parallel layers. A particulate sample, such as illustrated
in Fig. 3.10, clearly is not literally sub-divided into distinct identical “layers” that
the incident beam encounters sequentially. Dahm and Dahm proposed that for spectroscopic purposes, a particulate sample can be modeled as composed of a series of
layers, each one representative of the sample as a whole [16].
In envisioning a “representative” layer, it is instructive to consider the large and
small spherical particles included as shown in Fig. 3.10. Let us assume that the large
and small spheres that are of identical color have identical composition and differ
only in size. The diameter of the large spheres is twice the diameter of the small
Fig. 3.10 Particulate sample composed of particles with two different compositions, each in two
different sizes