Inverse-square law

You might have heard of what’s known as the inverse-square law. This law says that the intensity of many types of physical phenomena decreases with the square of the distance to the origin. For example, if you get twice as far from a lightbulb, a handheld light meter will register a four-fold drop in luminance.But… why? Wouldn’t it be more natural if the intensity dropped in direct proportion to how far you are from the source? Or, if it’s about scattering in a three-dimensional space, shouldn’t it be the cube of distance? Let’s try to figure it out.The making of a sphereIf we want an answer that doesn’t merely kick the can down the road, we need to start with the formula for the surface area of a sphere. From school, you might recall that the equation is:That said, I bet your teachers have never explained where the formula comes from. And as with many other “obvious” concepts in elementary mathematics, the answer is not as obvious as it seems — even though it’s been known since the…