The inverse square law defines the relationship between the irradiance or illuminance from a point source and distance. It states that the intensity of light per unit area is inversely proportional to the square of the distance from the source (essentially the radius).
In other words, if you measure 16 W/m² at 1 meter, you will measure 4 W/m² at 2 meters and 1W/m² at 4 metres, as shown in the image on the right. An alternate form of this equation which is sometimes more convenient is:
Distance is measured from the test point to the first luminating surface - the filament of a clear bulb, or the glass envelope of a frosted bulb.
Example
You measure 10.0 lm/m² from a light bulb at 1.0 meter. What will the flux density be at half the distance?
The inverse square law is only truly valid in cases where the light approximates a point source. A general rule of thumb to use for irradiance measurements is the five times rule: the distance to a light source should be greater than five times the largest dimension of the source. For a clear enveloped lamp, this may be the length of the filament. For a frosted light bulb, the diameter is the largest dimension of the bulb.
The graph below shows the relationship between irradiance and the ratio of distance to source radius. Note that for a distance 10 times the source radius (5 times the diameter), the error from using the inverse square is exactly 1%, hence the 'five times' approximation.
Note also, that when the ratio of distance to source radius decreases to below 0.1 (1/20 the diameter of the source), changes in distance hardly affect the irradiance (< 1 % error). This is due to the fact that as the distance from the source decreases, the detector sees less area, counteracting the inverse square law. The graph above assumes a cosine response. Radiance detectors restrict the field of view so that the d/r ratio is always low, providing measurements independent of distance.
Related Links
- Lighting - the Electronic Textbook
- http://www.saud.ku.edu/book/contents.htm
