inverse-square law of light
/ IN-vurss square /
Why does a candle that lights up a room look like a faint point from across a valley? As light leaves a source, it spreads out in all directions, thinning as it goes. The inverse-square law is the precise rule for that thinning: the brightness you receive drops with the square of the distance. Go twice as far and the light is not half as bright but a quarter; go ten times as far and it is a hundredth as bright.
The reason is pure geometry. Imagine the light from a star expanding outward as an ever-growing sphere. The total power is fixed, but it has to cover the whole surface of that sphere, and a sphere's surface area grows with the square of its radius. So at distance r, the same power is spread over an area proportional to r squared, and the flux falling on any one square meter must shrink as one over r squared. Nothing is lost — the light is just diluted over a larger and larger shell.
This single law is the linchpin of cosmic distance measurement. If you know how powerful a source truly is (its luminosity) and you measure how bright it looks (its flux), the inverse-square law converts the dimming directly into a distance. This is exactly how 'standard candles' work, from Cepheid variable stars to Type Ia supernovae, building the cosmic distance ladder out into the far universe. It assumes the light travels through empty space; in reality, dust along the way absorbs some of it, which must be corrected for.
Take two identical 100-watt bulbs, one at 1 meter and one at 3 meters. The far one looks not three times fainter but nine times fainter (three squared). Astronomers run this backward: knowing the 'wattage' of a standard candle, they read its faintness as a distance.
Brightness falls as 1 over distance squared — the geometric key to measuring cosmic distances.
The law assumes light travels unobstructed through empty space. Interstellar dust dims and reddens the light along the way, so real measurements must subtract this extinction before trusting the inverse-square distance.