All electrical laws
Inverse square law of illumination
The illuminance on a surface is directly proportional to the luminous intensity of the source and inversely proportional to the square of the distance between them.
E = I / d²
- E
- illuminance on the surface (lux)
- I
- luminous intensity of the source (candela)
- d
- distance from source to surface (metres)
In plain English: Light spreads out over a growing sphere, so double the distance and the same light covers four times the area — a quarter of the brightness. Same geometry as Coulomb's and gravity's inverse squares.
Where you'll meet it: Lux-level design for rooms and streets, photography exposure, and every 'find the illuminance under the lamp' numerical in the Utilization paper.
Calculators that use this law
Components this law governs
LED (light-emitting diode)Illuminance from the LED falls as 1/d², which is why a bright indicator is blinding at 10 cm and invisible across a lit room.Photodiode / PhototransistorThe illuminance reaching the die falls as 1/d², so doubling the distance to the source quarters your signal.PIR / Motion SensorThe infrared energy reaching the element falls as 1/d², which is why detection range is a real limit and the Fresnel lens exists to claw it back.Ultrasonic Distance SensorEcho strength falls with distance the same way light does, which is why cheap modules stop being reliable past a couple of metres.Optical Fiber & ConnectorsFree-space light spreads as 1/d²; a fibre's entire purpose is to stop that, which is why fibre loss is quoted in dB per kilometre instead.Incandescent / Halogen LampIlluminance falls as 1/d², which is why a desk lamp beats a ceiling fitting for reading despite far fewer watts.