Inverse-square law
Light, sound, gravity and radiation spreading from a point weaken with the square of distance: twice as far, a quarter as strong.
The inverse-square law says that something spreading out evenly from a small source gets weaker in proportion to the square of the distance. The reason is geometry. The same energy is shared over the surface of an ever larger sphere, and the area of a sphere grows with the square of its radius.
So doubling your distance from a lamp leaves you with one quarter of the light; three times as far gives one ninth; ten times as far, one hundredth. The same rule applies to the gravity of a planet, the brightness of a star, the loudness of an explosion in open air and the radiation from a radioactive source, which is why simply stepping back is one of the best forms of protection.
Astronomers use the law in reverse. If you know how bright a star really is, how faint it looks tells you how far away it is.
The law has conditions, and forgetting them is the usual mistake. It holds when the source is small compared with the distance, and when nothing along the way absorbs or scatters the energy. A laser, a car headlight or a radio dish concentrates its output into a beam and does not fade in the same way; nor does sound channelled along a tube.
See it in action
Coming up in future stories
- The Glowing Blue Powder That Poisoned a City 1987 · Goiânia, Goiás, Brazil
- The Woman Who Measured the Universe for 30 Cents an Hour 1908–1912 · Harvard College Observatory, Massachusetts