  We consider the problem of radiative transfer in stellar atmospheres where
the index of refraction departs from unity and is a function of density and
temperature. We present modified Feautrier and Lambda-iteration methods to
solve the equation of radiative transfer with refraction in a plane parallel
atmosphere. These methods are general and can be used in any problem with 1-D
geometry where the index of refraction is a monotonically varying function of
vertical optical depth. We present an application to very cool white dwarf
atmospheres where the index of refraction departs significantly from unity. We
investigate how ray curvature and total internal reflection affect the limb
darkening and the pressure-temperature structure of the atmosphere. Refraction
results in a much weakened limb darkening effect. We find that through the
constraint of radiative equilibrium, total internal reflection warms the white
dwarf atmosphere near the surface ($\tau \wig< 1$). This effect may have a
significant impact on studies of very cool white dwarf stars.
