Abstract
In the work, rays are considered which issue from the edge of a parabolic screen and after reflection from the convex side of the screen proceed in some fixed direction. Formulas are given for computing the trajectory and divergence of such rays. It is shown that for parabolic screens there exists a certain limit direction which has the character of a caustic boundary.
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Literature cited
V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Problems of the Diffraction of Short Waves [in Russian], Moscow (1972).
H. Hönl, A. Maue, and K. Westpahl, The Theory of Diffraction [Russian translation], Moscow (1964).
A. Erdelyi, Asymptotic Expansions, Dover (1961).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Maternaticheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 117, pp. 112–122, 1981.
The work on this problem was carried out under the constant attention of V. B. Filippov to whom the author expresses his sincere thanks.
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Graunov, O.V. Edge rays inside a bounded parabolic screen. J Math Sci 24, 334–340 (1984). https://doi.org/10.1007/BF01086992
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DOI: https://doi.org/10.1007/BF01086992