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.