# Abbe number

Abbe’s number is a dimensionless number that corresponds to the ratio of the optical refractive ability to the chromatic dispersion of a transparent material at visible wavelengths. In optics and lens design, the Abbe number, also known as the V-number or constringence of a transparent material, is an approximate measure of the material’s dispersion (change of refractive index versus wavelength), with high values of “V” indicating low dispersion. It is named after Ernst Abbe (1840-1905), the German physicist who defined it. The term V-number should not be confused with the normalized frequency in fibers.

Abbe numbers are used to classify various types of glass and other transparent materials according to their ability to disperse visible light, i.e. to spatially separate the different colors of a non-monochromatic light ray. Typical values can range from about 20 for very dense flint glass to more than 85 for particularly light crown glass. Given the definition as the ratio of differences of refractive indices in the visible, the dispersion properties quantified by the Abbe number are useful to classify materials only in this spectral range.

## Abbe number applications

Abbe numbers are used to classify different types of glass and other transparent materials according to their ability to scatter visible light, that is, to spatially separate the different colors of a non-monochromatic beam of light. Typical values can range from about 20 for very dense flint glass to more than 85 for very light crown glass. Since it is defined as the ratio of the differences in refractive indices in the visible, the dispersion properties quantified by the Abbe number are useful for classifying materials only in this spectral range.

It can be very useful to construct an Abbe diagram, in which the refractive index is plotted as a function of the Abbe number, in order to categorize glasses according to their position in the diagram.

The Abbe number is used to calculate the radii of curvature and focal lengths of individual lenses in achromatic doublets to minimize chromatic aberration.

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