  Gravitational and plasma lensing share the same mathematical formalism in the
limit of geometrical optics. Both phenomena can be effectively described by a
projected, two-dimensional deflection potential whose gradient causes an
instantaneous light deflection in a single, thin lens plane. We highlight the
differences in the time-delay and lensing equations that occur because plasma
lensing is caused by a potential directly proportional to the deflecting
electron number density and gravitational lensing is caused by a potential
related to the deflecting mass density by a Poisson equation. Since we treat
plasma and gravitational lensing as thin-screen effective theories, their
degeneracies are both caused by the unknown distribution of deflecting objects.
Deriving the formalism-intrinsic degeneracies for plasma lensing, we find that
they are analogous to those occurring in gravitational lensing. To break the
degeneracies, galaxies and galaxy-cluster scale strong gravitational lenses
must rely on additional assumptions or complementary observations. Physically
realistic assumptions to arrive at self-consistent lens and source
reconstructions can be provided by simulations and analytical effective
theories. In plasma lensing, a deeper understanding of the deflecting electron
density distributions is still under development, so that a model-based
comprehensive lens reconstruction is not yet possible. However, we show that
transient lenses and multi-wavelength observations help to break the arising
degeneracies. We conclude that the development of an observation-based
inference of local lens properties seems currently the best way to further
probe the morphologies of plasma electron densities. Due to the simpler
evidence-based breaking of the lensing degeneracies, we expect to obtain
tighter constraints on the local plasma electron densities than on the
gravitationally deflecting masses.
