  We present the manifestly covariant Lagrangian of a massless polarized
particle, that implies all dynamic and algebraic equations as the conditions of
extreme of this variational problem. The model allows for minimal interaction
with a gravitational field, leading to the equations, coinciding with Maxwell
equations in the geometrical optics approximation. The model allows also a wide
class of non minimal interactions, which suggests an alternative way to study
the electromagnetic radiation beyond the leading order of geometrical optics.
As a specific example, we construct a curvature-dependent interaction in
Schwarzschild spacetime, predicting the Faraday rotation of polarization plane,
linearly dependent on the wave frequency. As a result, the Schwarzschild
spacetime generates a kind of angular rainbow of light: waves of different
frequencies, initially linearly-polarized in one direction, acquire different
orientations of their polarization planes when propagate along the same ray.
