There are two parameters in the one-term Sellmeier formula for refractive index. Two different ways are proposed to express them in terms of the number of electrons, the dielectric constant, and the first excitation energy of the molecule. In the normal-dispersion region, one construction will make the formula an upper bound and the other, a lower bound. Furthermore, if a measured value at a particular frequency is used for the determination of the parameters, then the Sellmeier formula is an upper bound for frequencies below that reference frequency and a lower bound for frequencies above it. The various bounding properties are illustrated for the case of atomic hydrogen.
K. T. TANG, "One-Term Sellmeier Formula for Dispersion of Dilute Gases," J. Opt. Soc. Am. 62, 644-648 (1972)