Faraday rotation at quantum well exciton resonances is enhanced in a m
icrocavity due to multiple round-trips of light between the mirrors wh
en the cavity mode is strongly coupled to the exciton and is accompani
ed by resonant redistribution of the signal between right- and left-ci
rcular polarization. A resonant Faraday rotation of about 3 degrees is
detected in reflected light from an (In,Ga)As/GaAs quantum well micro
cavity in an 11.25 T magnetic field when the cavity mode is resonant w
ith either heavy- or light-hole excitons.