- Inverse-square law
physics, an inverse-square law is any physical lawstating that some physical quantityor strength is inversely proportional to the square of the distancefrom the source of that physical quantity.
Areas of application
In particular the inverse-square law applies in the following cases: doubling the distance between the light and the subject results in one quarter of the light hitting the subject.
Gravitation is the attraction between two objects with mass. This law states:
: "The gravitation attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation distance. The force is always attractive and acts along the line joining them".
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 Bullialdusbut put on a firm basis by Isaac Newtonafter Robert Hookeproposed the idea in a letter to Newton. Hooke later accused Newton of plagiarism.
The force of attraction or repulsion between two electrically charged particles, in addition to being directly proportional to the product of the electric charges, is inversely proportional to the square of the distance between them; this is known as
Coulomb's law. The deviation of the exponent from 2 is less than one part in 1015. [citation | last=Williams, Faller, Hill |title=New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass |url=http://prola.aps.org/abstract/PRL/v26/i12/p721_1 |journal= Physical Review Letters|volume=26 |pages=721-724 |year=1971] This implies a limit on the photonrest mass.
Light and other electromagnetic radiation
intensity(or illuminanceor irradiance) of lightor other linear waves radiating from a point source(energy per unit of area perpendicular to the source) is inversely proportional to the square of the distance from the source; so an object (of the same size) twice as far away, receives only ¼ the energy(in the same time period).
More generally, the
irradiance, "i.e.," the intensity(or power per unit area in the direction of propagation), of a spherical wavefrontvaries 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
Sunis 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 sourcefor 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
radiographyand radiotherapytreatment planing, though this proportionality does not hold in practical situations unless source dimensions are much smaller than the distance r.
The inverse-square law is used in
acousticsin measuring the sound intensityat a given distance from the source. [http://hyperphysics.phy-astr.gsu.edu/hbase/acoustic/invsqs.html Inverse-Square law for sound] ]
Let the total power radiated from a point source, "e.g.," an omnidirectional
isotropic antenna, be . At large distances from the source (compared to the size of the source), this power is distributed over larger and larger spherical surfaces as the distance from the source increases. Since the surface area of a sphere of radius is , then intensityof radiation at distance is::::
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
intensityof radiation, whether it is electromagneticor 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).
acoustics, the sound pressure of a spherical wavefrontradiating from a point source decreases by 50% as the distance is doubled, or measured in dB it decreases by 6.02 dB. The behaviour is not inverse-square, but is inverse-proportional::::
However the same is also true for the component of
particle velocitythat is in-phase to the instantaneous sound pressure .:
Only in the
near fieldthe quadraturecomponent 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 intensityis 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".
Field theory interpretation
irrotational vector fieldin three-dimensional space the law corresponds to the property that the divergenceis zero outside the source. Generally, for irrotational vector field in "n"-dimensional Euclidean space, inverse ("n" − 1)th potention law corresponds to the property of zero divergence outside the source.
Kepler's first law
* [http://www.sengpielaudio.com/calculator-distance.htm Damping of sound level with distance]
* [http://www.sengpielaudio.com/calculator-distancelaw.htm Sound pressure p and the inverse distance law 1/r]
Wikimedia Foundation. 2010.
Look at other dictionaries:
inverse square law — or inverse square law n. Physics a general principle of light, sound, gravity, etc. in which the intensity of energy coming from a given point varies inversely with the square of the distance from that point (Ex.: as the distance from a point… … English World dictionary
inverse-square law — atvirkštinių kvadratų dėsnis statusas T sritis fizika atitikmenys: angl. inverse square law vok. umkehrquadratisches Gesetz, n rus. закон обратных квадратов, m pranc. loi de l’inverse du carré, f; loi de l’inverse carré, f … Fizikos terminų žodynas
inverse square law — noun Physics a law stating that the intensity of an effect changes in inverse proportion to the square of the distance from the source … English new terms dictionary
inverse square law — Physics, Optics. one of several laws relating two quantities such that one quantity varies inversely as the square of the other, as the law that the illumination produced on a screen by a point source varies inversely as the square of the… … Universalium
inverse square law — Physics, Optics. one of several laws relating two quantities such that one quantity varies inversely as the square of the other, as the law that the illumination produced on a screen by a point source varies inversely as the square of the… … Useful english dictionary
inverse-square law — noun any physical law, such as that of gravitation, in which a quantity varies inversely with distance from a source as the square of that distance … Wiktionary
Inverse Square Law — F/A/V law of physics stating that some physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity. Applied to light and sound in AV … Audio and video glossary
inverse square law — noun Date: 1921 a statement in physics: a given physical quantity (as illumination) varies with the distance from the source inversely as the square of the distance … New Collegiate Dictionary
inverse square law — the intensity of radiation is inversely proportional to the square of the distance between a point source and the irradiated surface … Medical dictionary
inverse square law — noun any mathematical relation which states that the intensity of an effect at a point B, due to a source A, varies inversely as the square of the distance AB … Australian English dictionary