  The scattering of light by water droplets can produce one of the most
beautiful phenomena in Nature: the rainbow. This optical phenomenon has
analogues in molecular, atomic and nuclear physics. Recently, rainbow
scattering has been shown to arise from the gravitational interaction of a
scalar field with a compact horizonless object. We show that rainbow scattering
can also occur in the background of a black hole with surrounding matter. We
study the scattering of null geodesics and planar massless scalar waves by
Schwarzschild black holes surrounded by a thin spherical shell of matter. We
explore various configurations of this system, analyzing changes in mass
fraction and radius of the shell. We show that the deflection function can
present stationary points, what leads to rainbow scattering. We analyze the
large-angle scattered amplitude as a function of the shell's parameters,
showing that it presents a non-monotonic behavior.
