In physics, an inverse-square law is any physical law stating that some physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity.
If we want to calculate the attraction between massive bodies, we need to add all the point-point attraction forces vectorially and the net attraction might not be exact inverse square. However, if the separation between the massive bodies is much larger compared to their sizes, then to a good approximation, it is reasonable to treat the masses as point mass while calculating the gravitational force.
This law was first suggested by Ismael Bullialdus but put on a firm basis by Isaac Newton after Robert Hooke proposed the idea in a letter to Newton. Hooke later accused Newton of plagiarism.
More generally, the irradiance, i.e., the intensity (or power per unit area in the direction of propagation), of a spherical wavefront varies inversely with the square of the distance from the source (assuming there are no losses caused by absorption or scattering).
For example, the intensity of radiation from the Sun is 9140 watts per square meter at the distance of Mercury (0.387AU); but only 1370 watts per square meter at the distance of Earth (1AU)—a threefold increase in distance results in a ninefold decrease in intensity of radiation.
Photographers and theatrical lighting professionals use the inverse-square law to determine optimal location of the light source for proper illumination of the subject.
The fractional reduction in electromagnetic fluence (Φ) for indirectly ionizing radiation with increasing distance from a point source can be calculated using the inverse-square law. Since emissions from a point source have radial directions, they intercept at a perpendicular incidence. The area of such a shell is 4πr2 where r is the radial distance from the center.
The law is particularly important in diagnostic radiography and radiotherapy treatment planing, though this proportionality does not hold in practical situations unless source dimensions are much smaller than the distance r.
The energy or intensity decreases by a factor of ¼ as the distance is doubled, or measured in dB it would decrease by 6.02 dB. This is the fundamental reason why intensity of radiation, whether it is electromagnetic or acoustic radiation, follows the inverse-square behaviour, at least in the ideal 3 dimensional context (propagation in 2 dimensions would just follow an inverse-proportional distance behaviour and propagation in one dimension, the plane wave, remains constant in amplitude even as distance from the source changes).
Only in the near field the quadrature component of the particle velocity is 90° out of phase with the sound pressure and thus does not contribute to the time-averaged energy or the intensity of the sound. This quadrature component happens to be inverse-square. The sound intensity is the product of the RMS sound pressure and the RMS particle velocity (the in-phase component), both which are inverse-proportional, so the intensity follows an inverse-square behaviour as is also indicated above:
The inverse-square law pertained to sound intensity. Because sound pressures are more accessible to us, the same law can be called the "inverse-distance law".
Inverse floaters tend to lose liquidity in bear market, market participant says. (Clark Wagner of First Investors Management)
Jul 25, 1994; Last September, Clark Wagner told a derivatives conference audience that secondary market liquidity for inverse floaters...
Inverse floaters still hot; AIG closes big long-dated swap. (AIG Financial Products, Dade County, Florida)(Market in Review)
Feb 09, 1994; In a busy week for the derivatives market, investors continued buying inverse floating-rate debt despite rising short-term...