= Solution
Flint glass is approximately optically isotropic without an applied <magnetic field>. A longitudinal <magnetic field> changes the motion of its bound <Electrons>: the magnetic part of the <Lorentz force> acts with opposite sense on the two circularly rotating components of a driven electronic oscillation. Their optical response, and hence their <refractive indices>, split. Equivalently, the transverse <permittivity tensor> acquires a field-odd antisymmetric contribution whose eigenvectors are opposite <circular polarizations>.
The resulting <circular birefringence> gives <Faraday rotation>. For a weak longitudinal bias it is linear in the field:
$$
\boxed{\rho=\Upsilon B_\parallel,\qquad\theta=\Upsilon B_\parallel L.}
$$
Here $\Upsilon$ is the <Verdet constant> and $L$ the path length. The <magnetic field> breaks <time-reversal symmetry>, which is why this rotation is nonreciprocal. Reversing the bias reverses the rotation; reversing propagation while keeping the bias fixed does not undo it when physical polarization directions are compared in fixed laboratory axes. A transverse magnetic bias can have different, higher-order effects; the setup here is the longitudinal <Faraday effect>.
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