The bottom line is that when the distance to the source is several times
the dimensions of the source, all of the terms but the first become
essentially insignificant and the expression reduces to the old familiar
inverse square relationship. When the distance to the source is equal
or nearly equal to the source dimensions, one gets a fairly complex
mathematical relationship. As I suspected in the first place, while it is
not an inverse square law, using the inverse square law would be useful
as a first approximation. i.e. if you double the distance, you would
not get 1/4 the intensity, but you would also not get half the intensity,
you would, in fact get something in between.
Since I am an experimentalist, I thought of digging up a foot candle meter
,collecting some data and doing a graph just to see how much the intensity
deviates from the inverse square law. If I can find the time, perhaps I will
try that.
Judy, I apologize for subjecting you to more of the "sugar cube law"
(or whatever you called it). Perhaps I should have sent this directly
to Dick Sullivan, but I thought it was of sufficient interest that
some other folks might like to know about it.
Finally, perhaps my advice should have been, " remember, a complex
mathematical relationship governs the light intensity at different
distances from a bank of FL bulbs, it would be advisable to run
a number of tests and keep a record of the results." Frankly, that
is what I did, but then, as I have said, I am an experimentalist.
Bob Schramm