Past exam of the optics and electrodynamics course of the University of Cambridge / 2022 / Section B / 4 / e

Keep the magnetic field fixed in the laboratory and exchange source and observer. The incident unpolarized light now meets $P_2$ first. In fixed transverse laboratory axes the backward glass map is still $R(\theta )$, not $R(-\theta )$: this is optical nonreciprocity of the Faraday effect. The order of the two polarizers is reversed, soThe reverse light intensity is thereforeFor the optimal forward setting $\theta =\pi /4$, it vanishes: the $45^{\circ }$ input selected by $P_2$ rotates to $90^{\circ }$ and is blocked by $P_1$. At a general field, $I_r+I_f=I_0/2$. The result assumes equal incident light intensities in the two experiments. Treating the glass as a reciprocal natural optical rotator would predict cancellation of its laboratory rotation on reversal and would give the wrong answer here.

Keep source, observer and magnetic field in their original places, but interchange the physical polarizers, including their pass-axis orientations. The forward order is then $P_2$, glass, $P_1$, so the new Jones matrix is again $P_{1}R(\theta )P_2$. ConsequentlyThis is the same intensity change as exchanging source and observer. At the field that maximizes the original forward transmission, the swapped arrangement blocks the beam. If both operations were performed together, the original order relative to propagation would be restored and so would the original transmission. The answer concerns exchanging the two differently oriented pass axes; simply relabelling two identical polarizers while leaving their axes fixed would not change the apparatus.