The Inverse Square Law

Marijuana Horticulture

by Jorge Cervantes

The relationship between light emitted from a point source (bulb) and distance are defined by the inverse square law. This law affirms that the intensity of light changes in inverse proportion to the square of the distance. Intensity = light output / distance sq

A 1000-watt standard metal halide emits from 80,000 to 110,000 initial lumens and 65,000 to 88,000 average (mean) lumens. One lumen is equal to the amount of light emitted by one candle that falls on one square foot of surface one foot away. Super halides emit 115,000 initial lumens and 92,000 mean lumens. A 1000-watt HP sodium emits 140,000 initial lumens, and a 600-watt HP Sodium emits 90,000; watt for watt, that’s seven percent more lumens than the 1000-watt HPS. Lumens received by the plant are much more important.

Lumens received are measured in watts-per-square-fot or in foot-candles. One foot candle equals the amount of light that falls on one square foot of surface located one foot away from one candle.

Watts-per-square-foot is easy to calculate, but is an enormous way to determine usable light for a garden. It measures how many watts are available from a light source in the area. For example, a 400-watt incandescent bulb emits the same watts-per-square-foot as a 400-watt metal halide. Mounting height is not considered in watts-per-square-foot; the lamps could be mounted at any height from four to eight feet. Nor does it consider PAR watts or efficiency of the bulb.

Calculating foot-candles or lux is a more accurate way to estimate the amount of light plants receive, but still lacks the precision of measuring how much light is used by plants. If you start with a bulb that is rated in PAR watts, using a foot-candle or lux meter will suffice.

To demonstrate how dim light intensity retards plant development, check out an outdoor vegetable garden. Have you ever planted 65-day broccoli that took 100 days to mature? Most gardeners have suffered this fate. Did the plants get full sun all day long? The seed vendor assumes seeds were planted under perfect conditions – full sun and perfect temperature range. Plants that received less PAR light matured slowly and produced less than plants getting full sun all day long. It is the same in an indoor marijuana garden; plants that receive less light grow poorly.