  We investigate the optical properties of the solar gravitational lens (SGL)
with respect to an extended source located at a large but finite distance from
the Sun. The static, spherically symmetric gravitational field of the Sun is
modeled within the first post-Newtonian approximation of the general theory of
relativity. We consider the propagation of monochromatic electromagnetic (EM)
waves near the Sun. We develop, based on a Mie theory, a vector theory of
diffraction that accounts for the refractive properties of the solar
gravitational field. The finite distance to a point source can be accounted for
using a rotation of the coordinate system to align its polar axis with the axis
directed from the point source to the center of the Sun, which we call the
optical axis. We determine the EM field and study the key optical properties of
the SGL in all four regions formed behind the Sun by an EM wave diffracted by
the solar gravity field: the shadow, geometric optics, and weak and strong
interference regions. Extended sources can then be represented as collections
of point sources. We present the power density of the signal received by a
telescope in the image plane. Our discussion concludes with considering the
implications for imaging with the SGL.
