Selection of Glasses for Three-Color Achromats

If two thin lens elements of two different glasses are combined into a thin two-element system, then the chromatic properties of the system may be described by the effective values of V [V=(N−1)/(NF−NC)], and P [P=(ΔN/NF−NC)]. The effective value, P¯, is a linear function of V¯. On a graph of P versus V, the straight line drawn through the points for two glasses is the locus of all possible effective values of V and P for combinations of these two glasses. By means of such a graph the effective value P¯ for a combination of two glasses may be matched to P of a third glass whose V differs from V¯ by a useful amount. An achromatic lens system of the three glasses may then be computed, which will have a common focal length for three wavelengths.