  We describe how the observed polarization properties of an astronomical
object are related to its intrinsic polarization properties and the finite
temporal and spectral resolutions of the observing device. Moreover, we discuss
the effect that a scattering screen, with non-zero magnetic field, between the
source and observer has on the observed polarization properties. We show that
the polarization properties are determined by the ratio of observing bandwidth
and coherence bandwidth of the scattering screen and the ratio of temporal
resolution of the instrument and the variability time of screen, as long as the
length over which the Faraday rotation induced by the screen changes by
$\sim\pi$ is smaller than the size of the screen visible to the observer. We
describe the conditions under which a source that is 100\% linearly polarized
intrinsically might be observed as partially depolarized, and how the source's
temporal variability can be distinguished from the temporal variability induced
by the scattering screen. In general, linearly polarized waves passing through
a magnetized scattering screen can develop a significant circular polarization.
We apply the work to the observed polarization properties of a few fast radio
bursts (FRBs), and outline potential applications to pulsars.
