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Is it right to say diffraction is a geometrical optics phenomena and scattering a wave physical effect? I am considering a finite-length conducting plane and supposing a wave hitting the surface and reflected upon. In my opinion in addition incident wave should excite current sources on the plane resulting in a traveling surface wave. Upon reaching the edge wave they should scatter; if I assume very thin edge, but in many literature its said diffraction of waves is occurring at the edges. What will be correct from a physics point of view?

Thanks

Muhammad
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  • see: https://physics.stackexchange.com/questions/731414/why-is-it-true-that-when-the-frequency-is-increased-the-spread-angle-of-the-int/731454#731454 and https://physics.stackexchange.com/questions/106363/huygens-principle-in-em-waves/106372#106372 and https://physics.stackexchange.com/questions/633842/diffraction-physics-v-parageometric-optics-whatever-happened-to-it with references – hyportnex Sep 28 '23 at 12:19
  • It's possible that you are using the term geometrical optics to mean something other than the standard meaning. I don't see anything in your question that invokes geometrical optics. Can you clarify what you mean by that term? Better, if I am correct: remove the references to geometrical optics and use some other description. – garyp Sep 28 '23 at 14:00

2 Answers2

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Geometrical Optics is what can be built on the assumptions that light travels through a homogeneous medium in a straight line, and that light bends at the interface between media in accordance with the laws of reflection and refraction. Standard thin and thick lens treatments are based on these assumptions and are classic pieces of geometrical optics.

Diffraction cannot be deduced from these assumptions and requires a wave treatment. It is not a phenomenon of geometrical optics. Likewise scattering.

Philip Wood
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There are certain aspects of diffraction that can be taken into account using a geometrical approach. I suggest checking Keller's paper "Geometrical Theory of Diffraction". Following, I copied the abstract of it:

The geometrical theory of diffraction is an extension of geometrical optics which accounts for diffraction. It introduces diffracted rays in addition to the usual rays of geometrical optics. These rays are produced by incident rays which hit edges, corners, or vertices of boundary surfaces, or which graze such surfaces. Various laws of diffraction, analogous to the laws of reflection and refraction, are employed to characterize the diffracted rays. A modified form of Fermat’s principle, equivalent to these laws, can also be used. Diffracted wave fronts are defined, which can be found by a Huygens wavelet construction. There is an associated phase or eikonal function which satisfies the eikonal equation. In addition complex or imaginary rays are introduced. A field is associated with each ray and the total field at a point is the sum of the fields on all rays through the point. The phase of the field on a ray is proportional to the optical length of the ray from some reference point. The amplitude varies in accordance with the principle of conservation of energy in a narrow tube of rays. The initial value of the field on a diffracted ray is determined from the incident field with the aid of an appropriate diffraction coefficient. These diffraction coefficients are determined from certain canonical problems. They all vanish as the wavelength tends to zero. The theory is applied to diffraction by an aperture in a thin screen diffraction by a disk, etc., to illustrate it. Agreement is shown between the predictions of the theory and various other theoretical analyses of some of these problems. Experimental confirmation of the theory is also presented. The mathematical justification of the theory on the basis of electromagnetic theory is described. Finally, the applicability of this theory, or a modification of it, to other branches of physics is explained.

This paper presents an asymptotic expansion of the exact solution of the wave propagation problem.

References

  1. Keller, J. B. (1962). Geometrical theory of diffraction. Journal of the Optical Society of America, 52(2), 116-130.
nicoguaro
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