Distance for Lux Illuminance from Watt

Illuminance, distance and power

Light from a point source follows the inverse-square law. Written out, that's E = I / d², where E is illuminance in lux, I is luminous intensity in candela, and d is the distance in metres. Move twice as far away and the illuminance falls to one quarter (1/4). If the source is a uniform isotropic emitter, the equivalent spherical illuminance becomes E = Φ / (4π·d²), so an 800 lm lamp sitting at 1 m gives you ≈ 63 lux spherical (800 / (4π·1²)).

Applications

Photographic lighting sets and film and TV production lean on this constantly. So does gallery and museum lighting, where the lux has to stay under preservation limits for paintings and textiles. It also shows up in industrial workplace illuminance compliance and in stage design.

FAQ

Why does halving distance quadruple the lux? The same flux has to cover an area that scales with d². Cut the distance in half and that area shrinks to one quarter, so the density you measure in lux jumps 4×.

What is the difference between lumen and lux? A lumen counts total light output. Lux counts lumens landing on each square metre of a surface. That's why a 1000 lm lamp can read very high or very low in lux, all depending on how far away it is and how tight the beam is.

What lux levels do museums use? The most sensitive works, like watercolours and textiles, are kept near 50 lux. Oil paintings usually sit around 150–200 lux. Sculpture and stone can take 300 lux or more.