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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. The Abbe number, V d   , {\displaystyle V_{\mathsf {d}}\ ,} of a material is defined as V d ≡ n d − 1   n F − n C   {\displaystyle V_{\mathsf {d}}\equiv {\frac {n_{\mathsf {d}}-1}{\ n_{\mathsf {F}}-n_{\mathsf {C}}\ }}} , where n C , {\displaystyle n_{\mathsf {C}},} n d , {\displaystyle n_{\mathsf {d}},} and n F {\displaystyle n_{\mathsf {F}}} are the refractive indices of the material at the wavelengths of the Fraunhofer's C, d, and F spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the human vision. Outside this range requires the use of different spectral lines. For non-visible spectral lines the term "V-number" is more commonly used. The more general formulation defined as, V ≡ n c e n t e r − 1 n s h o r t − n l o n g {\displaystyle V\equiv {\frac {n_{\mathsf {center}}-1}{n_{\mathsf {short}}-n_{\mathsf {long}}}}} , where n s h o r t , {\displaystyle n_{\mathsf {short}},} n c e n t e r , {\displaystyle n_{\mathsf {center}},} and n l o n g , {\displaystyle n_{\mathsf {long}},} are the refractive indices of the material at three different wavelengths. The shortest wavelength's index is n s h o r t {\displaystyle n_{\mathsf {short}}} , and the longest's is n l o n g {\displaystyle n_{\mathsf {long}}} . Abbe numbers are used to classify glass and other optical materials in terms of their chromaticity. For example, the higher dispersion flint glasses have relatively small Abbe numbers V < 55 {\displaystyle V<55} whereas the lower dispersion crown glasses have larger Abbe numbers. Values of V d {\displaystyle V_{\mathsf {d}}} range from below 25 for very dense flint glasses, around 34 for polycarbonate plastics, up to 65 for common crown glasses, and 75 to 85 for some fluorite and phosphate crown glasses. Abbe numbers are used in the design of achromatic lenses, as their reciprocal is proportional to dispersion (slope of refractive index versus wavelength) in the wavelength region where the human eye is most sensitive (see graph). For different wavelength regions, or for higher precision in characterizing a system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used. Abbe diagram An Abbe diagram, also called 'the glass veil', is produced by plotting the Abbe number   V d   {\displaystyle \ V_{\mathsf {d}}\ } of a material versus its refractive index   n d   . {\displaystyle \ n_{\mathsf {d}}~.} Glasses can then be categorised and selected according to their positions on the diagram. This can be a letter-number code, as used in the Schott Glass catalogue, or a 6 digit glass code. Glasses' Abbe numbers, along with their mean refractive indices, are used in the calculation of the required refractive powers of the elements of achromatic lenses in order to cancel chromatic aberration to first order. These two parameters which enter into the equations for design of achromatic doublets are exactly what is plotted on an Abbe diagram. Due to the difficulty and inconvenience in producing sodium and .... Discover the Abbe Alexander popular books. Find the top 100 most popular Abbe Alexander books.