The Kirchhoff diffraction formula with small wavelength

[zhouhao]

Homework Statement

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.

Homework Equations

$U(P)=\frac{ia}{2\lambda}\int_S\frac{e^{ik(s+r)}}{sr}[(cos(n,r)-cos(n,s)]dS$

The Attempt at a Solution

when $\lambda$(wavelength) is very small,the $U(P)$ would very large and seems not equal to $\frac{ae^ir_{P_0P}}{r_{P_0P}}$

 

[Charles Link]

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.