section_path: Scientific work/Optics
section_name: Optics
paragraph_text: Optics
  
  Gauss's calculations enabled instrument maker Johann Georg Repsold in Hamburg to construct a new achromatic lens system in 1810. A main problem, among other difficulties, was the nonprecise knowledge of the refractive index and dispersion of the used glass types. In a short article from 1817 Gauss dealt with the problem of removal of chromatic aberration in double lenses, and computed adjustments of the shape and coefficients of refraction required to minimize it. His work was noted by the optician Carl August von Steinheil, who in 1860 introduced the achromatic Steinheil doublet, partly based on Gauss's calculations. Many results in geometrical optics are only scattered in Gauss's correspondences and hand notes.
  
  In the Dioptrical Investigations (1840), Gauss gave the first systematic analysis on the formation of images under a paraxial approximation (Gaussian optics). He characterized optical systems under a paraxial approximation only by its cardinal points, and he derived the Gaussian lens formula, applicable without restrictions in respect to the thickness of the lenses.