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The Kirchhoff diffraction formula with small wavelength

  1. Apr 18, 2017 #1
    1. The problem statement, all variables and given/known data
    The fresnel-kirchhoff diffraction formula could explain diffraction,I think it should also produce the result with relatively small wavelength and large width slit in which case there is no diffraction.
    730px-_Kirchhoff_1a.svg.png
    2. Relevant equations
    ##U(P)=\frac{ia}{2\lambda}\int_S\frac{e^{ik(s+r)}}{sr}[(cos(n,r)-cos(n,s)]dS##

    3. The attempt at a solution
    when ##\lambda##(wavelength) is very small,the ##U(P)## would very large and seems not equal to ##\frac{ae^ir_{P_0P}}{r_{P_0P}}##
     
    Last edited: Apr 18, 2017
  2. jcsd
  3. Apr 19, 2017 #2

    Charles Link

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    One suggestion would be to try it for an observation point that is directly on axis, and use a circular aperture so that the diffraction equations are readily workable. I do expect the diffraction equations for small wavelength and large aperture would give very nearly a shadow when using a single point source on one side of the aperture, but the equations are cumbersome enough, that it might be somewhat difficult to show for the general case.
     
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