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On Babinet's Principle

Published online by Cambridge University Press:  20 November 2018

R. C. MacCamy
R. C. MacCamy*
Affiliation:
Carnegie Institute of Technology
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In acoustic and electromagnetic theory much use is made of what is called the Principle of Babinet (1). The principle states that the problems of diffraction by an aperture, S, in a plane screen and by a plane obstacle occupying the position S, are equivalent. It is the intent of this paper to indicate how this notion of equivalent boundary problems, for partial differential equations, can be extended to other situations.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 632 - 640
Copyright
Copyright © Canadian Mathematical Society 1958 

Footnotes

This work was sponsored in part by the Office of Naval Research contract N onr-222(25), University of California at Berkeley and in part by Air Force Office of Scientific Research contract AF-18(600)-1138, Carnegie Institute of Technology.

References

1. Baker, B. and Copson, E. T., Huygens' Principle (Oxford, 1950).Google Scholar
2. Carleman, T., Sur la résolution de certaines equations intégrales, Arkiv. for Mat., Astro, och Fys., 16 (1922), No. 26.Google Scholar
3. MacCamy, R. C., Linear boundary problems arising in the diffraction of water waves by surface obstacles, Part II, Technical Report No. 2, N. our-222(25) (University of California at Berkeley, Nov. 1955).Google Scholar
4. Rubin, H., The dock of finite extent, Comm. Pure and App. Math., 7 (1954), 317–344.Google Scholar