The introduction of the natural and the diapoint variables has simplified considerably the investigation of problems in the large, problems where we can give the eiconal in closed form, and therefore for each object ray the image ray. The author and H. Boegehold have, first together and then alone, investigated problems of this kind. The author sketches first once more his new method, and gives then a series of examples, such as the eiconal for the case where to each object point belongs a rotation symmetric caustic, the eiconal for sharp image formation of two surfaces, the eiconal in the case where there is perfect centric symmetry, and other examples which are discussed as far as the time limit permits.
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