  We investigate the optical properties of the solar gravitational lens (SGL)
in the presence of the solar corona. For this, we consider the combined
influence of the static spherically symmetric gravitational field of the
Sun---modeled within the first post-Newtonian approximation of the general
theory of relativity---and of the solar corona---modeled as a generic, static,
spherically symmetric free electron plasma. We study the propagation of
monochromatic electromagnetic (EM) waves through the solar system and develop a
Mie theory that accounts for the refractive properties of the gravitational
field of the Sun and that of the free electron plasma in the extended solar
system. We establish a compact, closed-form solution to the boundary value
problem and demonstrate that the presence of the solar plasma affects all
characteristics of an incident unpolarized light. The affected properties
include the direction of the EM wave propagation, its amplitude and its phase,
leading to a reduction of the light amplification of the SGL and to a
broadening of the corresponding point spread function. The wavelength-dependent
plasma effect is critically important at radio frequencies, where it
drastically reduces both the amplification factor of the SGL and also its
angular resolution. However, for optical and shorter wavelengths, the plasma's
contribution to the EM wave leaves the plasma-free optical properties of the
SGL practically unaffected. We discuss the applicability of the SGL for direct
high-resolution multipixel imaging and spatially-resolved spectroscopy of
exoplanets
