Extinction and dust properties in a clumpy medium
  (abridged) The dust content of the universe is primarily explored via its
interaction with stellar photons, producing interstellar extinction. However,
owing to the physical extension of the observing beam, observations may detect
scattered photons, resulting in a change in the observed (or effective)
extinction, depending on the spatial distribution of the dust and the
resolution of the instrument. We investigate the influence of clumpy dust
distributions on effective extinction toward embedded sources and those in the
diffuse ISM. We use Monte Carlo radiative transfer to examine effective
extinction for various geometries. By varying the number, optical depth and
volume-filling factor of clumps in models of spherical shells and the diffuse
ISM, we explore the evolution of extinction. Depending on the number of
scattering events in the beam, the extinction curve steepens in homogeneous
media and flattens in clumpy media. As a result, clumpy dust distributions can
to reproduce extinction curves with arbitrary R_v, the effective ratio of
total-to-selective extinction. The flattening `washes out' the 2175 \AA bump
and shifts the peak to shorter wavelengths. The mean R_v of a shell correlates
with the optical depth of an individual clump and the wavelength at which a
clump becomes optically thick. Similar behaviour is seen for edge-on discs or
tori. However, at grazing inclinations the combination of extinction and strong
forward scattering results in chaotic behaviour. Caution is therefore advised
when measuring extinction in, for example, AGN tori or toward SNIa or GRB
afterglows. In face-on discs, the shape of the scattered continuum changes with
clumpiness, however, unlike absorption features, individual features in the
scattering cross-sections are preserved. Finally, we show that diffuse
interstellar extinction is not modified by scattering on scales of a few kpc.
