Light Dispersion And Particles

Another guess,

which reinforce the idea that $a_{\psi\,ne}$ is invisible or transparent.

$a_{\psi\,ne}$ shatters at the medium boundary.  Some particles recombine and give $a_{\psi}\ge a_{\psi\,ne}$ up till $a_{\psi}\le a_{\psi\,\pi}$

Since, particles of size $a_{\psi}\ge a_{\psi\,ne}$ require recombination to form, they are expected to be of lower number density (lights of lower intensity).

...anymore guesses and physics is a TV game show...