Gauss invented an algorithm for certain arithmetical purposes, which has various applications in optical problems. For instance, it is sometimes of value to see how the focal length, magnification, and back focus of a lens system vary with the change of one of the construction elements (thickness, radius, or refractive index). It is sometimes very useful to have explicit expressions for these significant lens characteristics as functions of the construction elements. However, the usefulness of these Gaussian brackets is not limited to Gaussian optics. The image errors for finite rays in the new form recommended by the author can be expressed with their help.
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