  Plasma lensing events can have significant observational consequences,
including flux density modulations and perturbations in pulse arrival times. In
this paper we develop and apply a formalism that extends geometrical optics to
describe the effects of two dimensional plasma lenses of arbitrary shape. We
apply insights from catastrophe theory and the study of uniform asymptotic
expansions of integrals to describe the lensing amplification close to fold
caustics and in shadow regions, and explore the effects of image appearance and
disappearance at caustics in the time of arrival (TOA) perturbations due to
lensing. The enhanced geometric optics approach successfully reproduces the
predictions from wave optics and can be efficiently used to simulate
multifrequency TOA residuals during lensing events. Lensing will introduce
perturbations both in the way the residuals change as a function of frequency
and also in the magnitude and sign of the residuals averaged over a frequency
band. The deviations from the expected dispersive $\nu^{-2}$ scaling will be
most significant when including observations at low frequencies. We examine the
consequences of lensing in the context of precision pulsar timing and touch on
its potential relevance to the study of FRBs.
