The inverse square law

Relation between luminous intensity (l) and illuminance (E)

The inverse square law

The illuminance on a point in a plane perpendicular to the direction of light incidence is equal to the luminous intensity in that direction divided by the square of the distance between the light source and the point in question. If we call this distance h, the following formula applies :

For example, if a point light source emits a luminous intensity of 100cd in a direction perpendicular to a surface at a distance of3 metres, the illuminance (E_p) at the point where the light strikes the surface will be 100/3²= 11 lux. If the surface is at a distance ofmetres from the light source, the illuminance will be : 100/2² = 25 lux.

This relationship is called the 'inverse square law'. Strictly speaking, it is only valid for point sources. In practice, however, the law holds good approximately as long as the distance between the light source and point of calculation or measurement is more than three times the longest dimension of the light source. For laboratory measurements on luminaires, on the other hand, the distance should be at least five to ten times the longest dimension of the luminaire.