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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 / 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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