  There are three widely-used conditions for characterizing negative refraction
in isotropic dielectric-magnetic materials. Here we demonstrate that whilst all
the different conditions are equivalent for purely passive media, they are
distinct if active media are considered. Further, these criteria can also be
applied to negative refraction in acoustic materials, where we might replace
the dielectric permittivity $\epsilon$ with a bulk modulus $\kappa$, and the
magnetic permeability $\mu$ with the mass density $\rho$.
