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# Optical Distance Law

## Geometric dilution of light vs. distance.

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)

where

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)

Since

E1 d12= E2d2 2 = constant (2)

(2) can be modified to

E1 / E2= d2 2 / 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/ d2 2

= (2500 lux) (2 m)2/ (5 m)2

= 400 lux

### Cosine law of Illumination

E = Φ / d2cos θ                 (3)

where

θ = angle between light source vertical line and sight line

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## Citation

• The Engineering ToolBox (2003). Optical Distance Law. [online] Available at: https://www.engineeringtoolbox.com/optical-distance-law-d_353.html [Accessed Day Month Year].

Modify the access date according your visit.

4.10.13

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