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Old 11-10-2010, 07:55 PM   #26
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The inverse square relationship of PAR and distance only works within a relatively small range of distances. When you get close to the bulb it breaks down. I determine relationships like this by just plotting the data on log-log graph paper. If the points form a straight line, it demonstrates that one variable is a function of a power of the other variable, with the slope of the straight line being the power.

It is very hard to measure distances very accurately with tests like this, and PAR meter readings can fluctuate as you read the meter, and vary from hour to hour. So each data point can be assumed to have a pretty large uncertainty. Considering all of that, if a line with a slope of minus 2 will fit the data points reasonably closely within the distance range that is relevant for aquariums, it is a good approximation to assume the inverse square relationship. Then, when you toss in values for multiple bulb fixtures, using the PAR number divided by number of bulbs, and those data points follow the same line, you can see that it is a good approximation to say that n bulbs give n times the PAR of one bulb.

It makes no difference to us, when we are looking for an aquarium light, whether or not the PAR varies with square of distance at distances of 1 inch to 4 inches, so I never bothered to measure it at those distances, except with single LEDs. Single LEDs are so near a point source that the inverse square relationship will hold true at even 3-4 inches from the single LED. It gets much more complicated when you have an array of LEDs.
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