Dispersive lensing and shadows in RN-AdS spacetimes with dark energy and plasma: theory and observational constraints

We examine photon propagation, black hole shadows, and weak lensing in Reissner–Nordström Anti de Sitter (RN–AdS) spacetimes with Kiselev quintessence immersed in dispersive plasma. Using the effective optical metric and a finite distance bending prescription suited to non asymptotically flat geometries, we retain full nonlinear dependence on charge, cosmological curvature, quintessence, and plasma. For a homogeneous plasma and for a singular isothermal sphere profile, exact turning point conditions yield photon spheres, shadow observables, and an illustrative consistency comparison with very long baseline interferometric deviation windows for M87* and Sgr A*. The thin lens mapping provides a plasma renormalized Einstein angle and a reference description of magnification trends in the weak lensing regime. Over the explored parameter ranges, stronger dispersion and more negative cosmological curvature enhance bending and magnification, while the finite distance shadow size increases with plasma loading for the considered profiles. Electric charge reduces bending and magnification and tends to lower the shadow deviation, whereas larger quintessence normalization amplifies near field signatures. These trends help break degeneracies between refraction and geometry and offer a practical baseline for multi frequency tests of near horizon physics.