Lighting
Point-source illuminance and distance
- where
- illuminance (lx)
- luminous intensity in the ray direction (cd)
- source-to-surface distance (m)
Explain this equation
Gives the illuminance on a surface facing a small light source at a given distance. Use it for spotlights, downlights and point checks.
I_v is the luminous intensity in candela in the direction of the surface, taken from the photometric data. d is the distance from source to surface in metres, measured along the ray. E is the illuminance in lux on a surface square-on to the ray.
Light from a point spreads out over a sphere whose area grows with the square of its radius. Double the distance and the same light covers four times the area, so illuminance falls to a quarter.
1000 cd at 2 m gives 250 lx. At 4 m it drops to about 62 lx. Halve the distance and the illuminance goes up four times.
Watch out: use candela, not lumens. For off-axis points use the slant distance along the ray, not the mounting height; a tilted surface also needs a cosine correction. It suits sources that are small compared with the distance.
For a sufficiently small source illuminating a perpendicular surface, illuminance falls with the square of distance. Doubling the distance reduces the direct illuminance to a quarter.
Use candela in the relevant direction from the luminaire's photometric data. Distance must be squared; for an unknown distance, use d = √(I_v/E).
Enter your values to see the result.
Common mistake
Do not substitute lumens for candela, and do not use mounting height if the ray travels a longer slant distance.
Limits
Point-source approximation, direct light, surface perpendicular to incident ray, negligible absorption. Extended sources at close distances, reflections and tilted surfaces need fuller calculations.
Sources
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