Reflection and refraction at the boundary of a medium with negative group velocity

Mandelshtam's views on the role of informal physical arguments in deriving the geometric law of refraction are discussed. It is shown that Sivukhin's theorem allows reconciling different approaches to justifying the choice of the refracted wave vector. Wave reflection and refraction are considered for a periodically heterogeneous half-space. It is shown that the analogy between the Snell–Descartes refraction law and the properties of a wave propagating in a chain of discrete interacting elements and in a periodically heterogeneous space is incorrect. The principal role of the homogeneity of interfacing media is stressed. The only case that corresponds to the ‘purely’ negative refraction is that of a homogeneous refracting medium in which both the dielectric constant and the magnetic permeability are negative.