  In this work we examine refraction of light by computing full solutions to
axion electrodynamics. We also allow for the possibility of an additional
plasma component. We then specialise to wavelengths which are small compared to
background scales to determine if refraction can be described by geometric
optics. We also allow for the possibility of an additional plasma component. In
the absence of plasma, for small incidence angles relative to the optical axis,
axion electrodynamics and geometric optics are in good agreement, with
refraction occurring at $\mathcal{O}(g_{a \gamma \gamma}^2)$. However, for rays
which lie far from the optical axis, the agreement with geometric optics breaks
down and the dominant refraction requires a full wave-optical treatment,
occurring at $\mathcal{O}(g_{a \gamma \gamma})$. In the presence of
sufficiently large plasma masses, the wave-like nature of light becomes
suppressed and geometric optics is in good agreement with the full theory for
all rays. Our results therefore suggest the necessity of a more comprehensive
study of lensing and ray-tracing in axion backgrounds, including a full account
of the novel $\mathcal{O}(g_{a \gamma \gamma})$ wave-optical contribution to
refraction.
