formula called the Inverse Square law to try and work it out
As optics and light can at times be counter intuitive, perhaps it is useful to dive a bit deeper here.
First, we observe a perfect point source as below
The point source radiates in all directions, and we have spherical symmetry. When we place light detectors, the cameras, at any position on a sphere the measured light intensity will be identical. All light from the source passes through the sphere, which has a surface area proportional to r squared. This means that the light intensity as measured by our detector, placed at the sphere’s surface must be inversely proportional to r squared.
Now let’s have a look at a long line of light sources, similar to a luminescent tube or array of LED’s.
The symmetry has now changed to a long cylinder. The surface area of the cylinder is proportional to r, no longer r squared as in the point source, and we conclude that our light intensity as measured by a detector placed on the cylinder is inverse proportional to r. So the inverse r squared rule does not longer apply here, with the most commonly used sources for our hobby.
We can go one step further, we take a infinitely large flat plane filled with light sources.
In this case our symmetry will be represented by a box, and the light intensity hitting the detector at the surface of the box will not longer be dependent on the distance from light sources to detector.
Let’s now take the example of a 1 meter long tank, with an LED bar that measures 1 meter by 10 cm. Same holds for fluorescent tubes above the tank.
- When we observe from a very large distance, perhaps 10-100 meter, our light source will look very small, almost as a nearly perfect point source. In this case our first scenario applies and we can estimate that light intensity will be roughly (indeed a very simplified model) proportional to the inverse of the distance squared. But of course, not many tanks are this big.
- When we get closer, let’s say one meter or less, then our source look like a long line source, and following our second scenario we see the intensity roughly proportional to the inverse of the distance. Note, that this is the most relevant observation for our aquarium hobby.
- When we get really close to our light source, say 0.1 meter or less, then the observer sees more like a large flat plane (in two directions) with light emitters, and according to the third scenario we have a constant light intensity that is no longer dependant of the position of our detector.
The above is all simplified, but it does illustrate that there is no easy answer to light intensity at different distances. The most satisfying answer for our hobby would be to assume inverse proportional to distance, rather than inverse proportional to the square of distance that is sometimes assumed.
Also:
As we can see from the above, the light intensity in our tanks may have large variations, like 50% or more, depending on position under the light source and depth. While it is important to have at least a decent indication of our PAR, it usually does not make much sense to measure very accurately and a simple measurement with an iPhone or Android app is no less valuable than a measurement with an expensive professional PAR meter. There is no point in measuring very accurately when the measured intensity has very significant variations anyway depending on where we measure.
