Multiple Reflections in the Theory of the Faraday Effect

In the case of the transmission of linearly polarized light, of angular frequency w, through a single medium, surrounded by vacuum on both sides, Donovan and Medcalf have given an exact treatment of multiple reflections in the theory of the Faraday effect. For the purpose of treating transmission through more complicated systems, Piller showed that, for wc % w (where wc is the cyclotron frequency), the problem is amenable to a simpler analysis. In the case of thin samples, we have been able to obtain simple analytic results expressing the multiple reflection rotation as a simple multiple of the singlepass result. In particular, we show that the two models are in disagreement for the case of weak absorption In thin samples. We also present a generalization of the Donovan-Medcalf results to the case of three distinct media.