  We compute the gravitational birefringence of light as it undergoes
gravitational lensing. To this end we re-derive the Souriau-Saturnini equations
in the Schwarzschild metric and solve them numerically and perturbatively. Our
main result is an offset between the trajectories of the photons of opposite
polarisations, which grows with time. We also find an intriguing instability of
the spin component transverse to the momentum.
