  In this paper we study the combined effects of size and shape of small solid
state particles on the absorption, emission and scattering characteristics. We
use the statistical approach to calculate these optical properties. In this
approach the average optical properties of an ensemble of particles in random
orientation are represented by the average optical properties of an ensemble of
simple shapes. The validity of this approach is studied in detail for a uniform
distribution of hollow spheres where the fractional volume of the central
inclusion is varied. We apply the results to two different areas of interest,
i) infrared spectroscopy and ii) polarization of scattered light. The effects
of particle size and shape on the optical characteristics are discussed. We
compare the results using the distribution of hollow spheres with those
obtained by using randomly oriented spheroids. Also we compare the results with
observations and laboratory measurements. The distribution of hollow spheres is
very successful in reproducing laboratory measurements of the scattering angle
distribution of the degree of linear polarization for incident unpolarized
light of randomly oriented irregular quartz particles. Furthermore, we show
that we are able to derive the size distribution of dust grains by fitting the
measured degree of linear polarization using computational result for hollow
spheres. It is shown that the distribution of hollow spheres is a powerful tool
for studying light scattering, absorption and emission by cosmic dust grains
and in particular when large numbers of particle parameters need to be
considered since the computational demand of the distribution of hollow spheres
is small.
