The Inverse Square Law states that the power of such things like electromagnetic radiation, acoustic energy, gravity, etc. is inversely proportional to the distance from the source of the radiation.
As light leaves a point source it travels in linear waves that are, in effect, perpendicular to the source. As the light travels away from the source it becomes increasingly less bright. Inverse Square Law tells us that the intensity of light produced, drops inversely proportional to the distance squared.
So: Final Intensity in lumens= Initial Lumen Intensity/(Distance from Source) squared. L=L1/(D^2), where L=Lumens on stage, L1=Initial output, D=Distance
If lamp produces 16 lumens of light at 1 foot, at 2 feet it produces 4 lumens, at 4 feet it produces 1 lumen... by 10 feet it produces only 0.16 lumens.
This is a real problem if your stage is 100 feet from your lighting position. lighting instruments are designed to produce extremely high initial light output using reflection (mirrors), refraction (lenses), and really high lumen output lamps.
Instruments with tighter beam angles produce a higher lumen output than instruments with wide beam angles. This is due to the higher concentration and uniform directionality of the beam of light. Thus, if you hung a 50˚ fixture next to a 5˚ fixture and both are the same distance from the stage, are the same fixture type (e.g., both are source fours), and have the same lamp in them, the 5˚ will be brighter.
This same inverse square principle holds true for acoustic energy whether it be emitted by an instrument, speaker, person, etc. The [[Sound Pressure Level]], measured in [[Decibels]] (dB-SPL), at the point of measurement is equal to the original SPL level divided by the square of the distance to the source. Thus SPL=SPL1/(D^2).
Sound can also behave as an inverse proportion, so someone might want to check my accuracy here.
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