= Solution
For independent <electronic transitions>, add the <electric dipole moment> responses:
$$
\boxed{\epsilon_r(\omega)=1+\sum_j\frac{S_j}{\omega_j^2-\omega^2-i\gamma_j\omega},\qquad S_j>0.}
$$
The positive constants $S_j$ include electron density and transition <atomic oscillator strength>. Each term adds an absorption peak to $\epsilon_r''$ and a dispersive positive-to-negative contribution to $\epsilon_r'-1$, as in the middle row of the figure.
Between well-separated absorption lines, where the medium is transparent, the <refractive index> generally increases with frequency: $dn_r/d\omega>0$, or $dn_r/d\lambda<0$. This is <normal dispersion>. Near a resonance the real response turns down with increasing frequency, producing an interval of <anomalous dispersion>, $dn_r/d\omega<0$, accompanied by appreciable absorption. The absorptive and dispersive parts are linked by the <Kramers-Kronig relations>; the steep variation is not independent of the loss spectrum.
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