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Explaining the Inverse Square Law
This is one of those nerdy topics that it helps to understand if you are building your own rig. It really is kind of important. I'm not interested in teaching the finer points, just enough so you can make educated decisions when changing your lighting systems. The Inverse Square Law applies to any wave: gravity, magnetic and of course, light. This short tutorial will help you understand how distance affects output, and help you overcome one of the most common mistakes that people make when dealing with light, ie: thinking that halving the distance to the item being lit will double the amount of light it gets. It seems common sense, but it is wrong. What I will do is try to show you by example.

For this example, assume we have a 40w incandescent flood (reflector lamp) light bulb shining on a green and white, checkerboard tile floor, and each tile is 12" x 12" (exactly one square foot). We could use any light or tile, this is just the easiest to work with and it keeps the math simple. We still start with the light at 2 foot away, then increase it to 4 feet away, ie: doubling the distance. When this imaginary bulb is 2 foot away, it shines on exactly 1 square foot of tile, as shown left. In the right image, we moved the bulb to 4 foot away (twice the distance) and it now covers the width of TWO tiles, twice as many as before This is why people instinctively think that doubling the distance will cut the light in half, but we are leaving out the other dimension.

Explaining the Inverse Square Law  Explaining the Inverse Square Law


So our light is cover twice as many tiles in width, but it also covers twice as many in depth. We have to double both the X axis as well as the Y axis, so now we are covering FOUR square feet instead of one, an increase of four times. We started with 40 watts of light covering one square foot, and by doubling the distance, we now have 40 watts of light cover four square feet. We went from 40w per square foot to 10w watts per square foot, exactly 1/4th the original power. The power on each square foot might not look 75% weaker, but you have to trust that it is.

Explaining the Inverse Square Law  Explaining the Inverse Square Law


This is all relative measurement, so it universally applies to any single bulb. When changing the distance, the amount of light that hits the item changes exponentially, not in a linear fashion. Here are some examples showing the math, and why it is called the Inverse Square Law.

2x further away = 1/4th the power because 22 = (2x2) = 4
4x further away = 1/16th the power because 42 = (4x4) = 16
7x closer = 49 times the power because 72 = (7x7) = 49

It is all relative to where you start. And you thought you would never use that math they taught in high school...

This doesn't mean that closer is always better, only that you always have the same amount of power coming from the lamp and that the further you are from the item, the larger the area you cover, but the lower the power per square foot/inch/cm. When you have multiple sources of light (as is always the case in curing) it gets more complicated, as you are getting wattage from multiple bulbs, but that is just extra math and the principle always holds true. The Inverse Square Law is called a "Law" for a reason. Whatever design you start with, you are very likely to tweak it over time, and if you remember this basic law, it will help keep you from getting surprised (or disappointed) with the results.

Here are some practical examples for growers:

Let's say you are using single bulbs to cover a few plants, but you want to cut the power in half. You don't double the distance because that would cut the power by 75%. Instead, you would move the bulb to around 1/2 again as far away. This means that if you started with the lamps at 3 feet away, you wouldn't go to 6 foot, you would take 1/2 of the 3 you started with, (1.5 feet) and add that to the distance, so you would be 4.5 feet away. At 4.5' away, the power will be 1/2 of the original power at 3'. (Remember that twice the distance would mean getting 1/4 the power, so to get it to 1/2 instead, you chop that extra 3 foot in half.)

Inversely, to double the power to the plant, you would move it 1/4 the distance and move it that much closer. 3 divided by 4 = 3/4 (9 inches) so you would move to 2 foot 3 inches away. (Remember that half the distance would be 4 times the power, so you divide that in half, and half of 1/2 the distance = 1/4 the distance)

Most growers only use UV lights once the plants are done with the vegetative state and are in the flowering state, however, most plants still grow some in the flowering state, so you might have to periodically adjust the light distance if you are running right at the edge of what the plants will tolerate. For growers looking to get the absolute maximum flavonoids or trichome production, this means adjusting the time or distance around once a week, once you have hardened their plants to the UV. Even if you don't remember the exact math, just remember that moving them closer to the lamp (or having them grow closer to the lamp) mean exponentially higher UV reaching the plant, so be careful.

Examples for UV curing:
Explaining the Inverse Square Law UV curing gets more complicated because you have multiple sources of light, and as get farther from the lamps, each square inch is likely to be covered by more bulbs, but less power from each. In a UV curing rig with many lamps (over 16), the overlap adds up to where the relationship is more linear up to a foot or two away. In a perfect setup, the distance between the lamps would either be exactly the same as the distance to the item, or a clean multiple. For example, if you are 4" away, you would have the lamps 4" apart, or 2" apart. This isn't critical for most applications, but it does allow for the most even distribution of UV. Another option is to have the lamps where they are basically touching each other, then the entire rig actions as one giant bulb. That is typically the best setup, and gets the fastest cures, but costs more to setup.

If you are running a rig with just a few lamps or with wide lamp spacing, then the above Inverse Square Law applies more directly. This is true of any rig for pool cues and the like, where you have one lamp per surfact, or any rig with lamps that are more than a few inches apart. These types of rigs are harder to manage because you really have to get the aiming right, as well as the timing. It isn't rocket science, but you have to dial them in a bit more to get the best results. Using a lot of lamps means the threshold is a big wide margin of error and you can't hardly do it wrong.

Hot spots
As this example shows, the light is hotter where the two cones of light overlap. It isn't exactly double, as some of the UV is ionized as heat due to "wave cancellation", however, that gets complicated to explain and isn't really an issue for the vast majority of UV curing rigs. The hot spots are relative to the distance to the item being cured, which is why I earlier stated that the distance between the lamps should be equal to or less than the distance to the item....or 1/2 that distance, so the hot spots overlap perfectly. When you have many lamps, it adds up. As long as you keep the lamps spaced tight enough, cold/hot spots aren't really an issue for 99% of you.

Sources include Wikipedia.

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