Distance from Source to Meter: d (feet)
Light Source Output: Lo (Lumens)
Light Meter measures Illuminance: I (foot-candles)
Area of Sphere: A = 4 p d2
Illuminance is the measurement of how bright a point source of light appears to the eye. It is measured in foot-candles (or lux). The foot-candle is defined as the illuminance on a uniform surface one foot away from the light of one candle and is equal to one Lumen/ft2. Which means a light source's output of 1 Lumen flowing through a sphere with a surface area equal to 1 ft2 would produce an illuminance of 1 foot-candle on the surface of the sphere.
Example: What light source output Lo (Lumens) would be required to produce an illuminance of 1 foot-candle at a distance of 1 foot?
Illuminance: I = Lo/A
where Lo is the Light Source Output (Lumens) and A is the surface area (ft2) of a sphere centered around the light source.
At a distance of 1 foot, A = 4 p ft2,
and so when I = 1 foot-candle,
Lo = IA = 4 p Lumens (approximately 12.57 Lumens)
In other words, for a light meter to read 1 foot-candle from a uniform point source of light that is 1 foot away, a light source of about 12.57 Lumens is required.
In general terms: I = Lo/(4 p d2) assuming the light can be considered a uniform point source (no reflector).
From this, one can determine a light bulb's minimum peak illuminance (foot-candles) when one knows its specified initial output rating (Lumens) and the distance (feet) to the observer. This is illustrated in the following graph showing the illuminance curves for lights of three different initial output ratings (in Lumens).
The nationally recognized standard of 0.1 foot-candles as a maximum level of light spillage off a property is indicated by the dotted line. If codes were designed to reflect this standard (or others), the formula for determining light placement could be as follows:
For a light bulb with an output rating of Lo (Lumens) and a code limiting illuminance to less than I (foot-candles), the minimum allowable distance from property line to the bulb would be d, where:
d = sqr_root(Lo / (4 p I))
This could be put into table form for those without a calculator handy. |