### Geometry factor for parallel light?

Posted:

**Sat Mar 03, 2018 9:48 am**Say we have a source of parallel light, described by a delta distribution like Le(x,w) = dirac_delta(w-w0)*f(x). This could be a "laser-like" source like I indicated in the pic below or an infinitely distant light.

Question is, when to add the 1/r^2 factor in the geometry term?

For illustration, my Gedankenexperiment:

*Case on lhs: Source projects a parallel beam. Its cross section is fixed. Even after going through the mirror. Thus the power received by the target in the bottom is independent of how far we take it away from the mirror. So I would omit the r-factor.

*Case on rhs: Light spreads out the further it goes away from the light source and/or the mirror. Decreasing power density must be accounted for by the r^-2 term.

So, tracing a path from a parallel source, I would omit the r^-2 term until the path hits a non-specular surface.

I wonder if I have the wrong idea in mind because I don't recall reading anything about propagating a "parallel beam flag".

Question is, when to add the 1/r^2 factor in the geometry term?

For illustration, my Gedankenexperiment:

*Case on lhs: Source projects a parallel beam. Its cross section is fixed. Even after going through the mirror. Thus the power received by the target in the bottom is independent of how far we take it away from the mirror. So I would omit the r-factor.

*Case on rhs: Light spreads out the further it goes away from the light source and/or the mirror. Decreasing power density must be accounted for by the r^-2 term.

So, tracing a path from a parallel source, I would omit the r^-2 term until the path hits a non-specular surface.

I wonder if I have the wrong idea in mind because I don't recall reading anything about propagating a "parallel beam flag".