  We derive, in a manifestly covariant and electromagnetic gauge independent
way, the evolution law of the electric field $E^\alpha = Ee^\alpha\ (e^\alpha
e_\alpha=1)$, relative to an arbitrary set of instantaneous observers along a
null geodesic ray, for an arbitrary Lorentzian spacetime, in the geometrical
optics limit of Maxwell's equations in vacuum. We show that, in general,
neither the magnitude $E$ nor the direction $e^\alpha$ of the electric field
(here interpreted as the observed polarization of light) are parallel
transported along the ray. For an extended reference frame around the given
light ray, we express the evolution of the direction $e^\alpha$ in terms of the
frame's kinematics, proving thereby that its expansion never spoils parallel
transport, which bears on the unbiased inference of intrinsic properties of
cosmological sources, such as, for instance, the polarization field of the
cosmic microwave background (CMB). As an application of the newly derived laws,
we consider a simple setup for a gravitational wave (GW) interferometer,
showing that, despite the (kinematic) shear induced by the GW, the change in
the final interference pattern is negligible since it turns out to be of the
order of the ratio of the GW and laser frequencies.
