  Future high precision photometric measurements of transiting extrasolar
planets promise to tell us much about the nature of these systems. We examine
how atmospheric lensing and (projected) planet oblateness/ellipticity modify
transit light curves. The large density gradients expected in planet
atmospheres can offset the unfavorably large observer-lens to source-lens
distance ratio, and allow the existence of caustics. Under such conditions,
starlight from all points in the planet's shadow is refracted into view
producing a characteristic slowing down of the dimming at ingress (vice versa
for egress). A search over several parameters, the planet radius etc., cannot
produce a nonlensed transit light curve that can mimic a lensed light curve.
The fractional change in the diminution of starlight is approximately the ratio
of atmospheric scale height to planet radius, expected to be 1 % or less.
Planet oblateness induces an asymmetry to the transit light curve about the
point of minimum flux, depending on the planet orientation. The fractional
asymmetry is around 0.5 % for a projected ellipticity of 10 %, independent of
lensing. For favorable ratios of planet to star radius, the above effects are
potentially observable with future space-based missions. This will allow us to
constrain the planet shape, and its atmospheric scale height, density and
refractive coefficient, providing information on its rotation, temperature and
composition. For HD 209458b, the only currently known transiting extrasolar
planet, caustics are absent because of the very small lens-source separation.
Finally, we provide estimates of other variations to transit light curves that
could be of comparable importance, including rings, satellites, stellar
oscillations, star spots, and weather.
