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Optical Distance Law

Geometric dilution of light vs. distance.

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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 / d2                  (1)


E = light intensity, illumination (lux, lumen/m2)

Φ = the quantity of light emitted by a lamp or a light source - luminous flux (lumen, lm)

d = distance from light source (m)


E1 d12 = E2 d22 = constant                   (2)

(2) can be modified to

E1 / E2 = 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

E1 = (10000 lumens) / (2 m)2

   = 2500 lux

The illumination intensity at distance 5 m can be calculated by modifying (2b) to 

  E2 = E1 d12 / d22 

     = (2500 lux) (2 m)2 / (5 m)2

     = 400 lux

Light intensity vs. distance from source

Cosine law of Illumination

E = Φ / d2 cos θ                 (3)


θ = angle between light source vertical line and sight line

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