  Radiation pressure and photon momentum in negative-index media are no
different than their counterparts in ordinary (positive-index) materials. This
is because the parameters responsible for these properties are the admittance,
sqrt(epsilon/mu), and the group refractive index n_g of the material (both
positive entities), and not the phase refractive index, n=sqrt(epsilon*mu),
which is negative in negative-index media. One approach to investigating the
exchange of momentum between electromagnetic waves and material media is via
the Doppler shift phenomenon. In this paper we use the Doppler shift to arrive
at an expression for the radiation pressure on a mirror submerged in a
negative-index medium. In preparation for the analysis, we investigate the
phenomenon of Doppler shift in various settings, and show the conditions under
which a so-called "inverse" Doppler shift could occur. We also argue that a
recent observation of the inverse Doppler shift upon reflection from a
negative-index medium cannot be correct, because it violates the conservation
laws.
