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Gauss's contributions (Dioptriche Untersuchungen, 1840) to the "classical" optical theory (Gaussian optics, i.e calculations made under the paraxial approximation) are well known, but long before he published his known treatise he published a small article (1817) with much more impressive results. This article dealt with a qualitative and quantitive description of a new objective for telescopes that is designed to reduce chromatic aberration (the phenomena in which the dispersion of light results in confused colours of the image). This objective consisted of two lenses, and Gauss calculated the shape, refractive powers (refractive indexes) and spatial disposition of the two lenses that is required for maximal elimination of chromatic aberration.

What made me ask this question is the article "On the new form of the achromatic object-glass introduced by Steinheil" (1863, by Bond, George Phillips) which claims that the famous optician Steinheil constructed a new form of achromatic objective "according to the system of curves proposed by Gauss". In addition, I found in Gauss's Nachlass much material in optics (see Gauss's Werke, volume 11, part 1, pp. 117-171) which seems to deal with the problem of removal of chromatic aberration, but not enough comments about it.

I didn't find enough material about this aspect of his optical work in the literature, so I ask if anyone can give a more detailed explanation of what Gauss actually did.

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  • $\begingroup$ The following source indicates that the Steinheil was referring to an article Gauss had published in Zeitschrift fur Astronomie of Lindenau and Bohenberger 1817. Please see JStor page. My German is non-existent, but a google search for "zeitschrift für astronomie gauß 1817" should locate the original. $\endgroup$ – Nick Jun 29 '18 at 22:58
  • $\begingroup$ “Berechnung achromatischer Doppelobjektive” (including the 1817 paper) is discussed in §§60-64 of the Schaefer commentary linked at an earlier answer. $\endgroup$ – Francois Ziegler Jun 29 '18 at 23:02
  • $\begingroup$ Thanks, but i already know Schaefer's discussion. I look for a more historically-oriented and detailed summary by someone who knows well the history of achromatic doublets (i don't know german, so i need to do Google translate). In other words, i want to know what new ideas he introduced in his design of the doublet - how did he eliminate chromatic aberration? did he calculate an aspheric shape for his lens? and how to put this aspect of his work in his whole work in optics. Schaefer's treatise is very good, but it makes several assumptions about the reader's previous knowledge. $\endgroup$ – user2554 Jun 30 '18 at 6:55

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