  There is ongoing interest in adopting various tools and ideas from general
relativity for optical applications and the study of light propagation through
natural or engineered media. Here, the covariant kinematics of light
propagating through arbitrary dielectric media in curved space-times are
derived, allowing for analysis and tracing of congruences of light through
media that may smoothly vary in character between vacuum, positively
refracting, and negatively refracting; or null, timelike, and spacelike with
respect to the background metric. The kinematics are then used to generalize
the Raychaudhuri equation -- an important tool in general relativity that
describes the focus of a congruence. These results will be useful for the
analysis of optical devices, particularly those designed using transformation
optics, and serve as theoretical tools to study generalized concepts in general
relativity.
