Inverse-Square Law, explained.
An inverse-square relation makes intensity proportional to one divided by distance squared when power spreads uniformly over spherical surfaces.
Why it happens
Distance-one intensity is a supplied scale. At radius r it becomes that scale divided by r², while the spherical surface-area ratio is r².
An inverse-square relation makes intensity proportional to one divided by distance squared when power spreads uniformly over spherical surfaces.
Read the result
The distance-one scale stays fixed when distance changes. Intensity and spherical spreading area move inversely rather than both growing together.
A worked example
Double distance from an ideal point source
Leave source scale at one hundred and start at distance one.
Move to distance two and compare intensity twenty-five with area ratio four.
Move to distance four to obtain intensity 6.25, preserving the same source scale.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Distance-one intensity is a supplied scale. At radius r it becomes that scale divided by r², while the spherical surface-area ratio is r².
Where this idea is useful
A practical use
Check whether doubling source distance would quarter intensity under the relevant propagation assumptions.
A common misconception
“Twice the distance always means half the intensity.”
Uniform spherical spreading increases area with squared distance, giving a quarter of the intensity at twice the radius.
What this explanation leaves out
- Point-source far-field geometry, no absorption and uniform spreading are assumed. Extended emitters, obstructions and near-field effects can violate this relation.
Does the law apply next to every lamp?
No. The point-source and propagation assumptions can fail for extended emitters, near fields and obstructed or absorbing paths.
What geometry justifies the distance exponent in your application?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.