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.
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