\(OD_{\psi}=2a_ecos(\theta)\)
where \(\theta\) is the radiance angle from the line joining the two charges. Given a wavelength \(\lambda_\psi\) we have destructive interference at,
\((2n+1)\cfrac{\lambda}{2}=2a_ecos(\theta_D)\)
\(\theta_D=cos^{-1}(\left[2n+1\right]\cfrac{\lambda}{4a_e})\)
and constructive interference at,
\(n\lambda=2a_ecos(\theta_C)\)
\(\theta_C=cos^{-1}({n}\cfrac{\lambda}{2a_e})\)
for \(n=0,1,2,3...\). A plot of cos-1(x/4) where \(x=\cfrac{\lambda}{a_e}\) is provided below.
As frequency of \(\psi\) increases, the first destructive band (\(n=0)\) moves towards the middle plane between the two charges. But the equation for constructive interference suggests that there is constructive interference at \(\theta_C=90^{o}\). What is seen then is a bright band between two dark bands in the region between the two charges when \(f\) is high. When \(f\) is low, the dark bands are at lower values of \(\theta_D\), we see a one bright band in the middle.
The circles locates the relative positions of the charges. If we round off the edges the pattern looks like.
Where a single wide bright band is replaced with an oval that over laps into the dark band.
If this is true then electronic clouds are just optical illusions. Added to the effects of interference is the incident X-ray. X-ray diffraction is then the superposition of the intrinsic interference pattern and the effects of incident x-rays on an array of orbiting electrons.
