  In order to study the effect of dust extinction on the afterglow of gamma-ray
bursts (GRBs), we carry out numerical calculations with high precision based on
rigorous Mie theory and latest optical properties of interstellar dust grains,
and analyze the different extinction curves produced by dust grains with
different physical parameters. Our results indicate that the absolute
extinction quantity is substantially determined by the medium density and
metallicity. However, the shape of the extinction curve is mainly determined by
the size distribution of the dust grains. If the dust grains aggregate to form
larger ones, they will cause a flatter or grayer extinction curve with lower
extinction quantity. On the contrary, if the dust grains are disassociated to
smaller ones due to some uncertain processes, they will cause a steeper
extinction curve with larger amount of extinction. These results might provide
an important insight into understanding the origin of the optically dark GRBs.
