  We present a new determination of the dust content and
near-ultraviolet/optical extinction curves associated with a sample of ~8300
strong (equivalent width > 1A) Mg II absorbers, with redshifts 0.4<z<2.2,
identified in Sloan Digital Sky survey (SDSS) spectra of quasars. Taking into
account the selection effects that result from dust extinction, including the
reduction in the signal-to-noise ratio of an absorber appearing in a reddened
quasar spectrum, we find a stronger dependence of E(B-V) on absorber rest
equivalent width (EW) than in other published work. The dependence of the
median reddening on EW can be reproduced by a power-law model:
E(B-V)=.8+/-3*10-4 * EW^(3.48+/-0.3) for 1.0A<EW<5.0A. Observed Mg II samples,
derived from flux-limited quasar surveys, are shown to suffer from significant
incompleteness at the level of 24+/-4 per cent for absorbers with EW>1A and
34+/-2 per cent for absorbers with EW>2A. Direct determination of the shape of
the near-ultraviolet extinction curves for absorbers as a function of E(B-V)
show evidence for systematic changes in the form of the extinction curves. At
low E(B-V) (>0.05), the extinction curve is well represented by a Small
Magellanic Cloud-like extinction curve. For intermediate E(B-V)s (<0.2),
approximately a third of MgII absorbers show evidence for a 2175A feature
similar to that of the Large Magellanic Cloud. For the small number of high
E(B-V) (>0.3) absorbers, the majority of which exhibit strong CaII 3935,3970
absorption, there is evidence for a 2175A feature as strong as that found in
the Milky Way. Application of the new results on the dust content of strong Mg
II absorbers shows that dusty absorbers can account for a significant
proportion, up to a factor of two, of the observed overdensity of absorbers
seen towards Gamma-Ray Burst (GRB) sightlines, compared to sightlines towards
quasars in flux-limited samples. (Abridged)
