From: Jeff Foster (jfoster@uclink.berkeley.edu)
Date: 12/11/01-04:15:12 PM Z
something I found while searching on
google....
http://www.calgaryaquariumsociety.com/Articles/Light_Part_2.html
THE INVERSE SQUARE LAW
It is often written in aquarium literature that light follows the
inverse square law, so that if you double the distance from the bulb you
decrease the intensity of light by a factor of four.
This isn't true.
Not for any real light source anyway. It only holds true for a
point-source of light that radiates light in all directions equally. If
you direct the beam with a reflector, or if you build a light that is
not infinitesimally small, the inverse square law does not apply.
In fact, if you are less than one tube length away from the middle of a
fluorescent tube, light drops off at an approximately linear rate. That
is, if you are two feet away from a 4-foot tube, you receive half (not
one quarter) the light that you would receive if you are just one foot away.
And if you are in front of the middle of a whole bank of six or more
fluorescent tubes, the light intensity at two feet away is almost the
same as it is only one foot away! Especially if the bank of lights is in
front of a flat reflector. I won't bother going into the proof of this
(it requires some second year calculus) but think about it for a while
and you will realize that as you move away from the center of the
reflector, you receive more light from the sides, and this compensates
for the increasing distance. This works as long as you are still closer
to the center of the reflector than the reflector is wide.
So a multiple tube fluorescent light fixture (with a flat reflector)
produces a very even light throughout the depth of a tank. If you want
to defeat the inverse square law, get more tubes.
Another way to defeat the inverse square law is with a curved reflector.
A curved reflector can reflect the light from the bulb as parallel rays.
The best shape for this is a parabolic reflector, like the ones used in
searchlights. They produce a parallel light beam that does not dim
appreciably with distance, giving lights equipped with parabolic
reflectors a very long range. Parabolic reflectors are also used in
aquaria, mostly with metal halide bulbs. Such a combination produces an
intense light, but unfortunately the light doesn't spread over the tank
bottom very evenly. So a modified parabolic reflector is often used
instead, so that the light does spread enough to cover the bottom but
not so much that it gets wasted.
TOTAL INTERNAL REFLECTION
robert wrote:
> Sandy (et al.),
>
> I'm very curious about your mention that the inverse square law does not
> apply to a bank of fluorescent tubes. Might you explain a bit more, or even
> give the math (or a reference to it)?
> Also, I am exposing gum dichromate emulsion to a bank (so far, just two)
> of F40BL bulbs (is there another that might be better?), and wonder whether
> the type of balast I use makes any difference. As it is, the bulbs come on,
> but I'm having some problems with the gum not hardening. It is probably not
> the exposure, since I get a very readable (if faint) dichromate image, but
> at this point I wonder about everything.
>
> Any info from anyone would be appreciated,
>
> Robert Schaller
>
>
> on 12/11/01 10:30 AM, Sandy King at sanking@clemson.edu wrote:
>
>
>>Jeff Foster wrote:
>>
>>
>>
>>>so last night I went down to my shop and hooked up a ground wire to
>>>all three ballast (via the screw holding them to the wood top) and
>>>then to the ground on the ac cord. bingo - no delayed start and no
>>>flicker! very cool solutions. I looked closely at the wiring
>>>schematic on the ballast label and it does show a little ground
>>>symbol leading from the case...hmmm.
>>>
>>
>>Congratulations. Wiring schematics can be useful when all else fails!!
>>
>>
>>>thanks to all who supplied insight - now on to printing ( banding
>>>test - even with the inverse square law for light fall off....)
>>>
>>
>>Interestingly, the inverse square law only applies to point source
>>lights, not to a bank of fluorescent tubes being used very close to
>>the exposing plane, essentially functioning as a diffuse light
>>system. In other words, contrary to expectations, doubling the
>>distance of the tubes from 2" to 4" from the exposing plane will
>>*not* result in a 2X increase in exposure time. It will in fact be
>>far less, perhaps barely enough to even notice.
>>
>>Sandy King
>>
>>
>
>
-- --- Jeff Foster - SDA UNIX UC Berkeley CA
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