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On the Obliquity Function to be used in the Approximate Theory of Diffraction

Published online by Cambridge University Press:  24 October 2008

W. R. Harper
W. R. Harper
Affiliation:
Hutchinson Research Student, St John's College
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Extract

The solution of problems in diffraction by an elementary application of Huyghens's principle is discussed. The obliquity function is investigated, using the criterion that the formula used must give the right result when integrated for the case of an undiffracted plane wave. It is shown that this is satisfied for distant points by any function which makes the integrals converge, but that to satisfy it completely a constant obliquity function is necessary. This makes a consideration of the distant boundary essential, as the integrals do not converge in this case. It is shown that a boundary distributed in a Gaussian way is completely satisfactory. The integral for the case of diffraction by a straight edge is solved exactly, leading to the usual result. Finally, the results are discussed in relation to the teaching of the subject.

I am indebted to Dr H. Jeffreys and to Mr F. P. White for their interest in this paper; also to Mr N. F. Mott, who has contributed much to the course of its development.

Type
Articles
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 3 , July 1929 , pp. 289 - 303
Copyright
Copyright © Cambridge Philosophical Society 1929

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References

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* Throughout this paper we shall use the well-known method of representing a simple harmonic motion by a complex number, the modulus of which is equal to the amplitude of the vibration, and the argument equal to the phase. The incident wave is taken as having unit amplitude, and the phase uniform over the aperture.

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