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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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