aberration to first order. Note that 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 hydrogen lines, alternate definitions of the Abbe number are often substituted (ISO 7944). Rather than the standard definition, above, using the refractive index variation between the F and C hydrogen lines, an alternative measure using the subscript "e" takes the difference between the refractive indices of the blue and red cadmium lines at 480.0 nm and 643.8 nm (with ne referring to the wavelength of the mercury e-line, 546.073 nm). Other definitions can similarly be employed; the following table lists standard wavelengths at which n is commonly determined, including the standard subscripts employed. Derivation Starting from the Lensmaker's equation for a thin lens The change of refractive power P between the two wavelengths λshort and λlong is given by This is expressed in terms of the power Pc at λcenter by multiplying and dividing by The relative change is inversely proportional to V See also Abbe prism Abbe refractometer Calculation of glass properties, including Abbe number Glass code Sellmeier equation, more comprehensive and physically based modeling of dispersion References External links Abbe graph and data for 356 glasses from Ohara, Hoya, and Schott Dimensionless numbers Optics Glass physics