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Anomalous Dispersion

Cauchy’s dispersion formula is applicable to normal dispersion of many transparent media in the visible region of the spectrum. In general, the refractive index decreases with increase in wavelength. But, over small wavelength regions, the refractive index increases with increase in wavelength accompanied by increased absorption of the radiation.

Increase in refractive index with increase in wavelength is termed as anomalous dispersion. It is noticed that anomalous dispersion is present at those wavelengths corresponding to the absorption bands of the medium. For example, in the case of sodium vapour in the visible region, anomalous dispersion is noticed at wavelengths 5890 Å and 5896 Å.

The curves AB, CD and EF show normal dispersion. However at the absorption wavelengths λ₁ and λ₂, the refractive index increases with wavelength. BC and DE represent anomalous dispersion. Iodine vapour has an absorption band in the visible region. When a hollow prism containing iodine vapour (called iodine prism) is used, red rays are deviated more than violet rays. Sellmeier’s formula for the refractive index of a medium is given by

Here A_p is proportional to the number of particles per unit volume vibrating with a natural frequency corresponding to wavelength λ_p, λ is the wavelength of the incident radiation. If the medium has two absorption wavelengths corresponding to λ₀ and λ₁, the Sellemeir’s relation will be

From this relation, it is clear that as λ approaches λ₀ or λ₁ from the shorter wavelength side, tends to –∞ at resonance. The curves obtained between and λ are shown in fig.

Cauchy’s dispersion formula is applicable for normal dispersion whereas Sellmeier’s formula explains both normal and anomalous dispersion.