The basic statement of The Inverse square Law is that the size of the force or the intensity of the radiation gets less as you move away from the sources – I guess that much is obvious. However the change is not simply proportional to the distance. The correct mathematical statement is that force or the intensity is proportional to the inverse of the distance squared.

This is a general law applying to and very useful in many applications. It is about the way a source of energy or a force spreads out from a point or small source. For instance it applies to gravity, heat, light and electric fields.

Who thought of it?

The first person to formulate and use this idea was Newton as he presented his theory of gravity to explain the orbit of the Moon around the Earth and the planets around the Sun.

Before Newton no one had been able to explain the role of gravity in the rotation of the planets but Newton showed mathematically that the force of gravity obeyed the inverse square law (see video below).

He gave the relationship that

F = GMm/r2

Where M and m are the two masses and r is the distance between their centres. G is a constant of proportionality known as the universal gravitational constant.

He said that the gravitational field spread out as the distance increased, not in two dimensions but in three dimensions:

Using the inverse square law for gravity to explain the change of force with distance.
Inverse square law for gravity

So because the area increases by the square of the distance any force field or radiation must spread out over that area and therefore must be less, proportional to 1/r2

The video below sets out to explain this with an unusual example:

Using a butter gun to explain the inverse square law

Other pages related to graphs and general physics ideas are: