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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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