From: Robkin, Eugene (erobkin@uwc.edu)
Date: 12/12/01-10:24:25 AM Z
I'll take a shot at separating the physics and the metaphysics in this and
expand a bit on Art's message.
The light from a point source follows the inverse square law. End of
statement. End of objectivity. This law is in no danger of being repealed
for photographic purposes.
Any light source sufficiently far away so that its largest dimension is
"small" compared to the viewing distance behaves like a point source.
Behaves like does not mean is. How much it behaves like a point source
depends on the sizes and distances and just how much the viewer cares about
it. This last means, just how accurate the viewer's measuring technology is
or, put another way, whether or not the departure from a pure point source
effect affects the viewer's application in a way that matters to the viewer.
Ahh, subjectivity enters.
A line source viewed from a nearby point out to about half its length looks
like a collection of point sources strung out in a line. The light observed
from some point away from the surface looks like the sum of the
contributions from the separate points. The sum is just the integral for
the calculus oriented. For a source of finite length this gives a light
intensity that varies like the reciprocal of the distance from the surface
plus an error term due to the fact that the line has finite length. The
error term is "small" for distances out to about half the light source
length. How important the error term is depends, as above, on the level of
concern and the measurement technology. The key here is that from any
single viewing point you are looking at the sum of the contributions from a
line of point sources. This result also breaks down if you are near or past
the end of the line source.
A plane source viewed from its surface out to some critical distance, which
I don't recall right off the bat, but I think it is something like half its
diagonal for sources that approximate squares, looks like a collection of
point sources spread over a surface. The light observed is again the sum of
the contributions from the individual points. Calculus enters here again
and you get constant intensity plus an error term. Repeat the above about
the error term including the fact that things are different outside the
boundary.
So get far enough away and all sources look like point sources. Get close
and the actual effect depends on the physical arrangement of the lights,
distances, how well you can measure things, and how much you care. For a 4
foot square light box anything from 0 out to a foot probably can't be
detected as far as the photography result is concerned and I'd bet that you
can get out to two feet or a little less before you'd see anything in the
print.
Your mileage will vary. That is the only guarantee since it appears that
everyone cares about different things.
Gene Robkin
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