The Inverse Square Law
The intensity of illumination due to a given source is inversely proportional to the square of the distance from the source.
As light travels away from the point source it spreads both horizontally and vertically and therefore intensity decreases. In practise this means that if an object is moved from a given point, to a point double the distance from the light source it will receive only a ¼ of the light (2 times the distance squared = 4).
For example, if an object at 10m from a light source receives 100 Lux, moving the object to 40m, it will receive only 1/16th of the light (4 times the distance, squared = 16) resulting in the object receiving only 6.25 Lux.
Using Multiple Illuminators
If the distance from a single illuminator is doubled then the intensity of the light is reduced by a factor of four. Therefore to achieve double the distance of one illuminator, achieving the same power on scene, 4 illuminators are required (2 squared = 4). Similarly to achieve 3 times the distance of one illuminator, 9 illuminators are required (3 squared = 9).
Practical Applications
In practice, there is no need to use multiple illuminators to achieve increases in distance. Tighter angle devices, or more powerful illuminators can provide the required additional power output.
