Schematic representation of plasma-lensing geometries. Grey disc stands for plasma lens, and darker region is for higher plasma medium. Panel a: Proposed model, showing frequency-dependent paths through the lens, where signals at frequencies ν₁ and ν₂ (black and red dot-dashed lines) encounter different electron densities. Panel b: Traditional model assuming frequency-independent paths. Solid lines show undeflected paths, α_i and θ_i denote the deflection angles and image positions (i = 1, 2), while Δd indicates the separation between observers.