  We propose and demonstrate cavity-enhanced polarization-rotation measurement
as a means to detect magnetic effects in transparent media with greater
sensitivity at equal optical disturbance to the medium. Using the Jones
calculus, we compute the effective polarization rotation effect in a
Fabry-Perot cavity containing a magnetic medium, including losses due to
enclosure windows or other sources. The results show that when measuring
polarization rotation, collecting the transmitted light has advantages in
simplicity and linearity relative to collecting the reflected light. We
demonstrate the technique by measuring Faraday rotation in a $^{87}$Rb atomic
ensemble in the single-pass and cavity-enhanced geometries, and observe
enhancement in good agreement with the theoretical predictions. We also
demonstrate shot-noise-limited operation of the enhanced rotation scheme in the
small-angle regime.
