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A Study of Harting’s Criterion for Complete Achromatism

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Abstract

If the glasses of an infinitely thin doublet obey Hartmann’s three-constant dispersion formula, complete achromatism can be attained on condition that the λ0 values of the two glasses be identical. This condition seems to have been first pointed out by Harting, and it is termed Hartings criterion herein. It can rarely be even approximately fulfilled in practice because the ν-values of realizable glasses would not be sufficiently different; this is shown by a plot of many current glasses and some obsolete ones. The relation of Harting’s criterion to König’s partial-dispersion criterion is discussed with a plot, as also is Lee’s suggestion that a plot of c versus n0 segregates the barium flints. Slevogt’s conclusions for the more general case when a is different for the two glasses are considered briefly. Fused silica and some crystals of possible use in optical systems are also discussed; their Hartmann constants for the visible and the ultraviolet regions are tabulated. Some of these materials have favorable characteristics in the visible region, but all that were studied fail in the ultraviolet just as do glasses in the visible.

© 1938 Optical Society of America

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