  We provide a general theoretical framework to describe the electromagnetic
properties of viscous charged fluids, consisting for example of electrons in
certain solids or plasmas. We confirm that finite viscosity leads to multiple
modes of evanescent electromagnetic waves at a given frequency, one of which is
characterized by a negative index of refraction, as previously discussed in a
simplified model by one of the authors. In particular we explain how optical
spectroscopy can be used to probe the viscosity. We concentrate on the impact
of this on the coefficients of refraction and reflection at the sample-vacuum
interface. Analytical expressions are obtained relating the viscosity parameter
to the reflection and transmission coefficients of light. We demonstrate that
finite viscosity has the effect to decrease the reflectivity of a metallic
surface, while the electromagnetic field penetrates more deeply. While on a
phenomenological level there are similarities to the anomalous skin effect, the
model presented here requires no particular assumptions regarding the
corpuscular nature of the charge liquid. A striking consequence of the
branching phenomenon into two degenerate modes is the occurrence in a
half-infinite sample of oscillations of the electromagnetic field intensity as
a function of distance from the interface.
