A square pyramidal frame, 18 inches square at its base and 34.5 inches tall, with grids of six-inch squares 11.5 inches apart, going from the tip to the base, allow you to illustrate the nature of an inverse square law.

A point source is one that emits radiation, or produces some type of field around it, that spreads uniformly in all directions. Such radiation or field obeys a law whereby its intensity, its flux per unit area, diminishes as the square of the distance from the source. In the frame in the photograph above, the first square is 11.5 inches from the point, where the source is. At twice this distance from the source, the radiation that has flowed through the first square has now spread to cover an area two squares on a side, or four times the area of the first square. At three times the distance, it now covers an area three squares on a side, or nine times the area of the first square. Thus, the intensity is inversely proportional to the square of the distance from the source. Technically, the edges of the squares in this frame should be curved to match the radius at which they sit, but it still shows very well the inverse square relation.

Various physical phenomena obey some type of inverse square law:

1) Light: The energy per area, E, called the illuminance, of a point source at some distance, r, goes as E = I/r², where I is the power or flux per solid angle (sometimes called the pointance). For radiant power, its units are watts per steradian, and for light, they are lumens per steradian, or candela. 1 lm/sr = 1 cd. The candela is defined as the luminous intensity, in a given direction, of a monochromatic source emitting at a frequency of 5.40 × 10¹⁴ Hz, that has a radiant intensity in that direction of 1/683 watt per steradian.

2) Gravity: The gravitational force between two objects is Gm₁m₂/r², where G is the universal gravitational constant (6.67 × 10^-11 N·m²/kg²). If we call the mass of earth m₁, then Gm₁/r² is g, the acceleration of gravity. When r = r_Earth, g is the value at the surface (on average), 9.81 m/s², which we can call g_Earth. As r increases, g decreases as the square; for example, at 2r_Earth, g = g_Earth/4, at 3r_Earth, g = g_Earth/9, etc.

3) Electric field (of a point charge): A point charge radiates an electric field that is spherically symmetrical, whose strength depends on the size of the charge, q, and the square of the distance from it, r. Its magnitude is E = q/(4πε₀r²), where ε₀ is the permittivity constant, which equals 8.854187818 × 10^-12 C²/N·m². E has the units of N/C. As for the examples above, if we call the magnitude of the field E at a particular distance r, then at 2r, the magnitude is E/4, at 3r it is E/9, etc.

4) Radiation (α, β and γ particles): Radioactive sources emit their radiation uniformly in all directions. Thus, the intensity of this radiation – the number of particles passing through unit area – decreases as the square of the distance. If we call the intensity I, I ∝ 1/r².

5) Sound (from a point source): Sound intensity also follows the inverse square law, assuming that no reflections interfere with the emitted sound wave. As above, if we call the intensity I, I ∝ 1/r².

References:

1) Inverse square law for light: http://hyperphysics.phy-astr.gsu.edu/hbase/vision/isql.html#c1
2) Power per solid angle: http://hyperphysics.phy-astr.gsu.edu/hbase/vision/photom.html#c1
3) The candela: http://hyperphysics.phy-astr.gsu.edu/hbase/vision/photom.html#c4
4) Gravity: http://hyperphysics.phy-astr.gsu.edu/hbase/Forces/isq.html#isqg
5) Electric field: http://hyperphysics.phy-astr.gsu.edu/hbase/Forces/isq.html#isqe
6) Radiation: http://hyperphysics.phy-astr.gsu.edu/hbase/Forces/isq.html#c4
7) Sound: http://hyperphysics.phy-astr.gsu.edu/hbase/Acoustic/invsqs.html#c1
8) Resnick, Robert and Halliday, David. Physics, Part One, Third Edition (New York: John Wiley and Sons, 1977), pp. 353-4.
9) Halliday, David and Resnick, Robert. Physics, Part Two, Third Edition (New York: John Wiley and Sons, 1977), pp. 568-70, 582-3, 586, 606-7.