  In this work, we derive two formulas encoding the polarization direction and
luminosity of synchrotron radiations from the moving electrons in curved
spacetime under the geometric optics approximation. As an application, we
further study the polarized images of synchrotron radiations from electron
sources in Schwarzschild black hole spacetime with a vertical and uniform
magnetic field. In particular, by focusing on the circular orbits of electrons
on the equatorial plane, we show the polarized images of the synchrotron
radiations from these orbits for different observational angles and discuss the
variations of the polarization directions concerning the angles.
