How do we measure light and how does it relate to my plant
Everyone has seen that our light bulbs are rated in lumens on the side of the package, that's how bright it is, right? Wrong! That is how bright it looks, lumens is a measure of how bright a light looks to our eyes, and it turns out that color matters, a 1W green LED looks way brighter than a 1W red LED, even though they are the same efficiency. We use the Luminosity function to convert light quantity to lumens. Lumens is good at estimating how easy it will be for you to see in a room with that light bulb, and that's about it. A more accurate method of measuring light is watts (how much energy is carried by the light) or mols/s (how many photons there are).
Plants use light for photosynthesis, and when calculating lighting requirements what we really care about is how fast will this light will make your plant grow. Well all plants and animals use the chemicals ATP and NADPH, and in plants photosynthesis takes light and makes these chemicals. Specifically when chlorophyll captures a photon it makes an electron, after it gets enough electrons the plant will produce some ATP and NADPH and that starts the process of it growing. If you're paying attention you noticed I said photons, that's the units plants use for growth. That means that growth of a plant is directly tied to photons captured, not watts or "brightness". It turns out that chlorophyll captures light at various efficiencies depending on the wavelength of the light (basically the color), and we can define a new unit of "brightness" based on how much of the light gets used in photosynthesis. We call this light photosynthetically active radiation (PAR) and we can define a function that converts from actual light amount (in watts or mols/s) to PAR Photon Flux (PPF) , just like was done with lumens. Since photosynthesis is in photons, we keep the units and PPF is in mols/s). And through some studies we measured the conversion curve for PPF and created the PAR action spectrum. If you look at it you'll see it dips in the middle with peaks at the side, while lumens peaks at the middle. That is why lumens is a bad unit for measuring light when growing plants, lumens measures how much greenish light there is, PAR measures non-greenish light, practically the opposite.
It's also important to note that the actual brightness of the bulb is irrelevant, it depends on the distance to the bulb and the fixture it's mounted it, that creates a certain amount of light on the leaf of your plant. The brightness is the light per unit area, if we are using lumens, then we measure the light at a given spot in lux, if we are using PPF, we measure the light at a given spot in PPFD (PPF Density). 1lux = 1 lumen per sq meter, 1 PPFD = 1 PPF per sq meter. These are the numbers that matter to your plant, since it's the brightness on the leaf.
Ok, so I need to use PAR, how many PPF/PPFD is my light bulb
The short answer is it depends, the long answer is you can estimate it if you know the spectrum. White bulbs are commonly rated by color tempreture. This rating really means that it looks like a light with that color temperature, for incandescents and halogen color tempreture is an accurate measure of spectrum, and you can use standard conversion ratios. For fluorescents it's not accurate, but fluorescents are mostly the same and you can estimate, for LEDs it depends a LOT on the type of LEDs and there isn't really a good way to get PPF unless it's either on the spec sheet or the specific LEDs used are known. This site has some tables for estimating the PPF if the Lux is known, but for a standard florescent, 1 lux = 0.0135 umol/(m^2*s). If you have LEDs, I would estimate is as a fluorescent light unless it is a purple LED grow light (I cover these below).
How much light does my plant really need?
When actually talking about total light for the plant what matters is the brightness at the leaf, in PPFD and the time the light is there, if you integrate the PPFD over the time you can get the Daily Light Integral (DLI), this is a measure of how much light hits the leaf in a day. Per the wikipedia "full sun" is 26 mol/day per sq meter. This paper says that where a VFT lives, it can exceed 40 mol/day per sq meter. That paper also has the DLI requirements for various plants, and basically all "full sun" plants will do excellent with a DLI over 20, and will grow fine with a DLI over 15 or so in a greenhouse. Most carnivorous plants are full sun plants, and that's probably where you should be aiming for lighting requirements, 15-20+ for a DLI, and it's not "too much" light until you're at a DLI of 45-50 (though I suspect many plants will do fine if it's even more, I have no evidence for this).
How do you calculate DLI? Well if you know the PPFD of your setup, DLI is (PPFD in umol/s*m^2) * (hours the light is on) * 0.0036. So a setup with a PPFD of 300 umol/s*m^2 and a photoperiod of 14 hours has a DLI of 15.12mol/day*m^2. Using the tables above for lux to PPFD, if this was a fluorescent lamp it would probably be 22,200 lux and that's about the lowest brightness that you'd want for a full sun plant (factor of 74).
How many bulbs do I need for my setup?
Well first you need to determine how big the area is that you need to light. Then you need to find the target DLI that you want and what photoperiod that you want to use to get to that DLI. The below formulas assume that all the light goes onto the target area (your pots), and none of it missed. It obviously depends on your planters and these formulas will generally underestimate the light.
In PAR, use this formula, PPF_required = (Target DLI/photoperiod in hours)*278*(area in sq meters), then divide PPF_required by the PPF rating of your lamps to get the number of lamps required.
In Lumens, use this formula, Lumens_required = (Target DLI/photoperiod)*278*(area in sq meters)*(PPFD to lux factor [74 for fluorescents]), then divide the lumens required by the lumen rating of your lamps to get the total required.
I got one light bulb, how close should it be to my pot
This depends a lot on the fixture, in the previous method we assumed that all of the light went to the plants. If you have just a single bulb then much of the question is how close does it need to be to get the right light level. For this you need to figure out the beam angle of the lamp/fixture, that is how much does the light spread out. If you have just an incandescent without a fixture then it lights up in all directions (360 degrees), but if you put it in a fixture that redirects all the light into a narrow beam then more light goes into that one direction (maybe 30 degrees). Then you calculate the area lit up, not the area of your pot and determine the PPFD/Lux using that area.
The formula for determining mounting distance is then as follows.
In PPF, Target_PPFD=(Target DLI/photoperiod)*278, mounting height (in meters) = sqrt(PPF_rating/Target_PPFD/pi)/tan(beam angle/2)
In Lumens, Target Lux = (Target DLI/photoperiod)*278*(PPFD to lux factor [74 for fluorescents]), mounting height (in meters) = sqrt(Lumen_rating/Target_Lux/pi)/tan(beam angle/2)
I still don't get it! Give me examples!
If you plan on using 48-inch fluorescent, and like everyone seems to recommend, you want T5HO bulbs. You use the Home Depot shelves to keep your plants, what kind of fixture should you use?
Well the shelf is 48x18 inches, for a total area of 864 sq in or 0.55 sq meter. You want a DLI of 20 when you have a photoperiod of 14 hours. Since these are standard fluorescents we can use the PPFD to Lux factor of 74 and calculate it. (Target DLI/photoperiod)*278*(area in sq meters)*(PPF to lux factor [74 for fluorescents]) = (20/14)*275*0.55*74=15,989 lumens. Your T5HO Bulb is about 4750 lumens. So you need 15989/5000 3.3 bulbs. I would probably use 4 per level, but 3 is probably enough to get by with, especially if you extend the photoperiod to 16 hours. These bulbs are 54W, so using 4 bulbs would get you to 216W of power to light up each level (it's a lot of juice!).
If you have a lamp with a known PPF rating such as this it has a PPFD of "2890umol" for 11 sq feet, most likely meaning per sq meter, giving the entire lamp a PPF rating of 2890umol/s. If you wanted to convert a room into an indoor greenhouse this could do it. If your room was 10x20 feet, then it would be 18.5 sq meters. To get a DLI of 20 with a photoperiod of 14 hours you would need: PPF_required = (Target DLI/photoperiod in hours)*278*(area in sq meters)=(20/14)*278*18.5=7,347umol/s, total number of lamps would be 2 or three lamps to light the whole room up. Three of them would use just under 1kW of power.
And this is why people use the LED grow lights, with the above fluorescent example you needed 216W for 0.55sq meter, or 392W/m^2, for the LED lights you get similar lighting levels with 1kW per 18.5sq meter, or 54W/m^2, a significant power reduction because the light use high effency LEDs and doesn't put out light the plants don't need.
More on those purple LED grow lights
Most LED grow lights don't list the PPF, they don't list the lumens. How do you determine if it's bright enough? The answer is you kinda have to guess. But I made a calculator to help with this.
First, look up the specs on your LED grow light, usually they list wattage and the LED type and count. I bought this one. It says 12W, with the following LEDs (all 1W), "Red (660 nanometers 3 peices; 630 nanometers 6 peices): Blue(460 nanometers 3 peices)".
First you need to estimate the actual power to the LEDs, it will ALWAYS be less than the LED power rating (in this case 1W). Use the rated power if you have to, but it's better to get a kill-o-watt and measure with that. In my case the bulb use 9.4W. Standard power supplies are about 80% efficient (rough estimate, and mostly depends on build quality and practically impossible to confirm without breaking it apart), that means there is about 9.4*0.8 or 7.5W send to the LEDs. Second the LEDs produce mostly heat, but a large chunk of the power is actual light. For the Cree 1W 660nm LED, it's roughly 40% of power is light, the rest is heat. Using that number you get 7.5W*0.4=2.96W of light output.
Now, using this calculator you can estimate actual PPF. Enter 2.96W of light, and you can enter the actual LED wavelengths by specifying "custom wavelength" for the color (this is in the form of <LED wavelength>:<LED count>, etc), for this light you would enter "660:3, 630:6, 460:3" as the custom spectrum. The calculator will estimate the actual spectrum and calculate the PPF and related values using the given spectrum. For this specific light, it gets you to the brightness level to achieve "full sun" when mounted to light a 6-8inch diameter pot. If you used this to light the home depot racks used above you'd need about 16 of these bulbs (and it would use about 50W less power).
So what does this all mean? How much light do I really need?
Most people are going to be using white lights, for most of these lights if using a standard light meter, you want roughly 20,000-35,000lux depending on the specific photoperiod you need to get "full sun" light. However this is NOT as bright as the sun which often exceeds 100,000 lux (so that upper limit is somewhat flexible). If you are using funny colored lights (LED grow lights), this is NOT the right number, and your light meter is useless (unless you have a very high end one that measures PPFD, these are $200+). In all cases PPF and PPFD are far better units for measuring light for plants than Lumens and Lux.