  The objective of this article is to build up a general theory of geometrical
optics for spinning light rays in an inhomogeneous and anisotropic medium
modeled on a Finsler manifold. The prerequisites of local Finsler geometry are
reviewed together with the main properties of the Cartan connection used in
this work. Then, the principles of Finslerian spinoptics are formulated on the
grounds of previous work on Riemannian spinoptics, and relying on the generic
coadjoint orbits of the Euclidean group. A new presymplectic structure on the
indicatrix-bundle is introduced, which gives rise to a foliation that
significantly departs from that generated by the geodesic spray, and leads to a
specific anomalous velocity, due to the coupling of spin and the Cartan
curvature, and related to the optical Hall effect.
