We calculate the radial surface brightness profile of the image of a gamma-
ray burst (GRB) afterglow. The afterglow spectrum consists of several power
-law segments separated by breaks. The image profile changes considerably a
cross each of the spectral breaks. It also depends on the density profile o
f the ambient medium into which the GRB fireball propagates. Gravitational
microlensing by an intervening star can resolve the afterglow image. We cal
culate the predicted magnification history of GRB afterglows as a function
of observed frequency and ambient medium properties. We find that intensive
monitoring of a microlensed afterglow light curve can be used to reconstru
ct the parameters of the fireball and its environment and provide constrain
ts on particle acceleration and magnetic field amplification in relativisti
c blast waves.