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)
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