We present a proof-of-concept study that dust extinction curves can be extracted from the infrared (IR), optical, ultraviolet (UV), and X-ray afterglow observations of GRBs without assuming known extinction laws. We focus on GRB 050525A (z = 0.606), for which we also present IR observations from the Spitzer Space Telescope at t = t_(IR) ≈ 2.3 days postburst. We construct the spectral energy distribution of the afterglow at t = t_(IR) and use it to derive the dust extinction curve of the host galaxy in seven optical/UV bands. By comparing our derived extinction curve to known templates, we see that the Galactic or Milky Way extinction laws are disfavored versus those of the Small and Large Magellanic Clouds (SMC and LMC), but that we cannot rule out the presence of a LMC-like 2175 A bump in our extinction curve. The dust-to-gas ratio present within the host galaxy of GRB 050525 A is similar to that found in the LMC, while about 10%-40% more dust is required if the SMC template is assumed. Our method is useful to observatories that are capable of simultaneously observing GRB afterglows in multiple wave bands from the IR to the X-ray.
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