Abbe number

The Abbe number V_d characterises the dispersion of an optical glass by comparing its refractive index at three Fraunhofer lines: the helium d-line (587.6 nm, yellow), the hydrogen F-line (486.1 nm, blue), and the hydrogen C-line (656.3 nm, red). The definition V_d = (n_d − 1)/(n_F − n_C) is dimensionless and reduces to about 30 for typical flint glasses (high dispersion), 60 for typical crown glasses (low dispersion), and can reach 95 for exotic low-dispersion fluorite-like materials used in premium camera telephoto lenses.

The Abbe number is the key design parameter for chromatic-aberration correction. An achromatic doublet combines a crown element (high V_d, weak dispersion) and a flint element (low V_d, strong dispersion) in the right proportions to cancel first-order chromatic aberration at two wavelengths. Apochromatic triplets use three elements of different V_d to cancel at three wavelengths, with residual aberration proportional to the fourth power of bandwidth. Ernst Abbe introduced this number at Zeiss in the 1880s as part of his systematic approach to lens design — the first truly industrial-mathematical optical engineering — and Abbe numbers remain the standard specification on every glass-manufacturer's datasheet today.