Inverse square law

  1. Hi all looking for a bit of advice me the misses and the kids are starting a indoor flower garden and some herbs for the kids now my problems have come down to the lighting I have found out the colour spectrums needed as well as the luminous intensity required for heathly plant growth but the problems with looking into this is it is mostly discussed on weed growing forums where I think a lot of brain cells have been lost from smoking what they grow.
    Now to what I need help with let's say I have a cfl (compact flourescent light) that puts out 2000 lumens now my understanding of the law (which is most probably wrong) is 1 lumen is classed I foot from the light covering 1 sq foot area of the sphear and as it gets further away the lumen gets weaker 1/4 1/9 ect but do the lumens become more if you get closer to the bulb as with a cfl you can put it 3" away from the plant sorry for the vagness and the length of post but any help would really be appriciated thanks
  2. jcsd
  3. jtbell

    Staff: Mentor

    In principle, yes, the inverse square law works in both directions. However, it assumes that the source "looks like" a small point at all distances that you are considering. When you get close enough to a real light bulb, it doesn't "look" small any more and the inverse-square law breaks down.

    How close is too close depends on how accurate you want to be, and on the size of the bulb.
  4. So what would it be then for 3" distance @ 2000 lumen and what would the formula be please
  5. sophiecentaur

    sophiecentaur 14,730
    Science Advisor
    Gold Member

    Hi and welcome to PF.
    The inverse square law only applies strictly when you have a 'point source' of light. Once you are far enough from the light source for it to look 'small', you can do the ISL calculation but, close up, it breaks down because the source covers a large range of angles from your measuring position. You will probably save a lot of time by just taking the practical advice you get from 'growing' forums.
    Growing weed requires very high levels of light - more than you would want to live with. You should get your advice from more conventional sites - like this one, I think. You will not, I imagine, be wanting high crop yield so the requirement for lighting will be much less - see the table in that link.

    If you can't find specific advice about the sort of layout and lamp powers you need (and I'm sure there will be several forums with ideas) then you can do a shirt cuff calculation. You can get an idea of the illumination level available - related to the foot candle figures in the link by adding up (inverse square law) the contributions from individual lamps in an arbitrary layout. With a good, white or crinkled tinfoil, reflector, you will get more than twice the useful illumination. (But you will have read a lot of stuff already, I imagine.) Having a single cfl very close to your plants would be bad value because of the contrast between light (close) areas and dim (further away) areas - hence my reference to an array with a reflector ('light box'?)

    PS Watch out for the loony sites about this topic. I think you will spot them. They have all sorts of unrealistic ideas about 'underground survival' farming. Fact is that most plants would be grown indoors under artificial light, if we could do better than sunlight! It's expensive, indoors.
  6. Thanks for that maybe I should have given some more information I have a choice of 15 x 30w 2000 lumen cfl bulbs (450w and 30000 lumen total) at 3" away covering a 4' sq area or a 600w 56000 lumen metal halide which due to heat from bulb needs to be about 3' from plants but still covering same area both situations will have reflectors and the area will be surrounded with Mylar a 95% reflective material so really just trying to work out the best lumen system to use based on the hight restrictions and a rough lumen/watt ratio landing on the plants for both systems thanks
  7. jbriggs444

    jbriggs444 2,235
    Science Advisor

    If the bulbs are 3 inches away from the plants then each individual bulb cannot cover the entire 4 foot square area evenly. It will be more than 3 inches away from some parts of the area (obviously). What you gain from the inverse square law because you are close to one plant, you lose because less area is brightly illuminated. It is a wash.

    So instead of looking at the inverse square law, you need to be considering what fraction of the bulb's light hits the plant bed and what fraction goes elsewhere. With reflectors around the bulbs and at the walls, that fraction is going to be reasonably close to 100%.

    That's the same for both the array of small bulbs and for the single large bulb. You can choose on a price per lumen or convenience basis and ignore the inverse square law in this case.
    Last edited: Aug 22, 2014
  8. If you put the bulb too close to the plant the heat will dry it out and kill it. That's a little wisdom from my high school experience of grow operations. Wait, I meant to say that a friend told me that would happen.
  9. sophiecentaur

    sophiecentaur 14,730
    Science Advisor
    Gold Member

    A big light box will give better results as the light will be spread evenly over more of the leaves. The plants will get just as much light if they are spaced not too far apart. Reflectors are 'free' to run, too. I have read that LEDs are better because they will not overheat the plants. Expensive, though.
  10. I haven't got problems with the heat off the cfl bulbs you can actually hold them when on as opposed to the metal halide which does get verry hot hence my post are the cfls going to be more lumen efficient being about 3" away without problems to the plants or will the metal halide be more lumen efficient although more lumens but being approx 3' away ?
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