The identification of the refractive index and the wave vector for general (possibly active) linear, isotropic, homogeneous, and nonspatially dispersive media is discussed. Correct conditions for negative refraction necessarily include the global properties of the permittivity and permeability functions $\epsilon =\epsilon \left(\omega \right)$ and $\mu =\mu \left(\omega \right)$ . On the other hand, a necessary and sufficient condition for left handedness can be identified at a single frequency $(\mathrm{Re}\epsilon ∕\mid \epsilon \mid +\mathrm{Re}\mu ∕\mid \mu \mid <0)$ . At oblique incidence to semi-infinite, active media, it is explained that the wave vector generally loses its usual interpretation for real frequencies.