  In this paper, we turn our attention to light propagation in
three-dimensional electrodynamics. More specifically, we investigate the
behavior of light rays in a continuous bi-dimensional hypothetical medium
living in a three-dimensional ambient spacetime. Relying on a fully covariant
approach, we assume that the medium is endowed with a local and linear response
tensor which maps field strengths into excitations. In the geometric optics
limit, we then obtain the corresponding Fresnel equation and, using well-known
results from algebraic geometry, we derive the effective optical metric.
