Optical Distance Law
Distance and geometric dilution of light
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The illumination intensity on a surface is inversely proportional to the square of its distance from the light source and can be expressed as
I = L / d2 (1)
where
I = light intensity, illumination (lux, lumen/m2)
L = luminance of lamp (lumen)
d = distance from light source (m)
Since
I1 d12 = I2 d22 = constant (2)
(2) can be modified to
I1 / I2 = d22 / d12 (2b)
Example - Illumination Intensity from a Lamp at distance
The illumination intensity from lamp with luminance 10000 lumens at distance 2 m can be calculated with (1) as
I1 = (10000 lumens) / (2 m)2
= 2500 lux
The illumination intensity at distance 5 m can be calculated by modifying (2b) to
I2 = I1 d12 / d22
= (2500 lux) (2 m)2 / (5 m)2
= 400 lux
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