A general expression for the complex Faraday rotation is obtained by generalizing the Kramers-Heisenberg dispersion formula. It shows that the pure rotation is proportional to the sum of circular dichroism in in all resonance transitions weighted by the appropriate resonance-dispersion factors. The cases of free ions and rare-earth ions in solids are discussed. It is shown how ${\mathrm{Gd}}^{3+}$ and ${\mathrm{Eu}}^{2+}$, having the same electronic structure, may possess very different rotatory powers in a given frequency range through the difference in their optical spectra. The formula for the anomalous rotatory dispersion about sharp lines is also given.

• Received 17 June 1963

DOI:https://doi.org/10.1103/PhysRev.133.A511