Optical Distance Law
The illumination intensity on a surface is inversely proportional to the square of its distance from the light source and can be expressed as
E = Φ / d 2 (1)
where
E = light intensity, illumination (lux, lumen/m 2 )
Φ = the quantity of light emitted by a lamp or a light source - luminous flux (lumen, lm)
d = distance from light source (m)
Since
E 1 d 1 2 = E 2 d 2 2 = constant (2)
(2) can be modified to
E 1 / E 2 = d 2 2 / d 1 2 (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
E 1 = (10000 lumens) / (2 m) 2
= 2500 lux
The illumination intensity at distance 5 m can be calculated by modifying (2b) to
E 2 = E 1 d 1 2 / d 2 2
= (2500 lux) (2 m) 2 / (5 m) 2
= 400 lux
Cosine law of Illumination
E = Φ / d 2 cos θ (3)
where
θ = angle between light source vertical line and sight line
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