  We study the effects of dust grain size on the spectral energy distribution
(SED) of spherical circumstellar envelopes. Based on the self-similarity
relations of dusty SEDs derived by Ivezic & Elitzur (1997), we expect an
approximate invariance of the IR SED for models with different grain sizes.
Approximate invariance follows from the fact that differently sized grains have
similar optical properties at long wavelengths where the dust reprocesses the
starlight. In this paper, we discuss what are the physical requirements on the
model parameters to maintain the approximate invariance of the IR SED. Single
grain size models are studied for a wide range of grain sizes in three optical
depth regimes. In this study, we find limits for the cases where the IR SED is
and is not capable of conveying information about grain sizes, and to what
extent it does so. We find that approximate invariance occurs for a much larger
range of grain sizes than previously believed, and, when approximate invariance
holds, the SED is controlled mainly by one parameter, the reprocessing optical
depth, a quantity that measures the fraction of starlight that is absorbed by
the dust grains. Models with a grain size distribution are studied as well. For
these models, we find that, in many instances, the concept of approximate
invariance may be extended from the IR SED to all wavelengths. This means that,
for a wide range of optical depths, models with different grain size
distributions will produce very similar SEDs and, hence, the reprocessing
optical depth is the only quantity that can be unambiguously obtained from the
SED. The observational consequences of this result are discussed in detail.
