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Information about Inverse Square Law

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This diagram shows how the law works. The lines represent the flux emanating from the source. The total number of flux lines depends on the strength of the source and is constant with increasing distance. A greater density of flux lines (lines per unit area) means a stronger field. The density of flux lines is inversely proportional to the square of the distance from the source because the surface area of a sphere increases with the square of the radius. Thus the strength of the field is inversely proportional to the square of the distance from the source.


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.

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 a quarter reduction of the light.

Gravitation

The gravitational attraction between two massive objects, in addition to being directly proportional to the product of their masses, is inversely proportional to the square of the distance between them; 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.

Electrostatics

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.[1] This implies a limit on the photon rest mass.

Light and other electromagnetic radiation

The intensity (or illuminance or irradiance) of light or 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 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 law is also particularly important in diagnostic radiography and radiotherapy treatment planing.

Acoustics

The inverse square law is used in acoustics in measuring the sound intensity at a given distance from the source.[2]

Examples

Electromagnetic radiation

For another example, 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 intensity I of radiation at distance r 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 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 follow a just 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

In acoustics, the sound pressure of a spherical wavefront radiating from a point source decreases by a factor of ½ as the distance is doubled, or measured in dB it would decrease 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 velocity that is in-phase to the instantaneous sound pressure .



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".

Field theory interpretation

For an irrotational vector field the law corresponds to the property that the divergence is zero outside the source.

This article contains material from the Federal Standard 1037C, which, as a work of the United States Government, is in the public domain.

See also

Notes

Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
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For a list of set rules, see .


A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior.
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Quantity is a kind of property which exists as magnitude or multitude. It is among the basic classes of things along with quality, substance, change, and relation. Quantity was first introduced as quantum, an entity having quantity.
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<noinclude> Inverse is the opposite of something. This word and its derivatives are used greatly in mathematics, as illustrated below. </noinclude>
  • Inverse element of an element x with respect to a binary operation * with identity element e

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proportionality, see Proportionality (disambiguation).


In mathematics, two quantities are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio.
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square of a number is that number multiplied by itself. To square a quantity is to multiply it by itself. Its notation is a superscripted "2"; a number x squared is written as x2.
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Distance is a numerical description of how far apart objects are at any given moment in time. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria (e.g. "two counties over").
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Gravitation is a natural phenomenon by which all objects with mass attract each other. In everyday life, gravitation is most familiar as the agency that endows objects with weight.
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Isaac Newton's theory of universal gravitation is a physical law describing the gravitational attraction between massive bodies. It is a part of classical mechanics and was first formulated in Newton's work Philosophiae Naturalis Principia Mathematica, published in 1687.
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Ismaël Bullialdus (September 28, 1605 - November 25, 1694) was a French astronomer.

Bullialdus was born Ismaël Boulliau in Loudun, Vienne, France, the first surviving son to Calvinists Susanna Motet and Ismaël Boulliau, a notary by profession and amateur
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Sir Isaac Newton

Isaac Newton at 46 in
Godfrey Kneller's 1689 portrait
Born 4 January 1643(1643--) [OS: 25 December 1642]
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Robert Hooke, FRS (July 18, 1635 – March 3, 1703) was an English polymath who played an important role in the scientific revolution, through both experimental and theoretical work.
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Coulomb's law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated as follows:

The magnitude of the electrostatic force between two points electric charges is directly proportional to the product of the magnitudes of each

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Photon

Photons emitted in a coherent beam from a laser
Composition: Elementary particle
Family: Boson
Group: Gauge boson
Interaction: Electromagnetic
Theorized: Albert Einstein (1905–17)
Symbol: or
Mass: 0[1]
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In physics, intensity is a measure of the time-averaged energy flux. To find the intensity, take the energy density (that is, the energy per unit volume) and multiply it by the velocity at which the energy is moving. The resulting vector has the units of power divided by area (i.e.
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illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of the intensity of the incident light, wavelength-weighted by the luminosity function to correlate with human brightness perception.
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Irradiance, radiant emittance, and radiant exitance are radiometry terms for the power of electromagnetic radiation at a surface, per unit area. "Irradiance" is used when the electromagnetic radiation is incident on the surface.
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Light is electromagnetic radiation of a wavelength that is visible to the eye (visible light). In a scientific context, the word "light" is sometimes used to refer to the entire electromagnetic spectrum.
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A point source is a single identifiable localized source of something. A point source has negligible extent, distinguishing it from other source geometries. Sources are called point sources because in mathematical modeling, these sources can usually be approximated as a
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energy (from the Greek ενεργός, energos, "active, working")[1] is a scalar physical quantity that is a property of objects and systems of objects which is conserved by nature.
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Irradiance, radiant emittance, and radiant exitance are radiometry terms for the power of electromagnetic radiation at a surface, per unit area. "Irradiance" is used when the electromagnetic radiation is incident on the surface.
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In physics, intensity is a measure of the time-averaged energy flux. To find the intensity, take the energy density (that is, the energy per unit volume) and multiply it by the velocity at which the energy is moving. The resulting vector has the units of power divided by area (i.e.
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In physics, power (symbol: P) is the rate at which work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time.
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Wave propagation is any of the ways in which waves travel through a medium (waveguide).

With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves.
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A sphere is a symmetrical geometrical object. In non-mathematical usage, the term is used to refer either to a round ball or to its two-dimensional surface. In mathematics, a sphere is the set of all points in three-dimensional space (R3
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:For the notion of wave front in functional analysis, see wave front set.


In optics and physics, a wavefront is the locus (a line, or, in a wave propagating in 3 dimensions a surface) of points having the same phase.
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In physics, absorption is the process by which the energy of a photon is taken up by another entity, for example, by an atom whose valence electrons make transition between two electronic energy levels. The photon is destroyed in the process.
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Scattering is a general physical process whereby some forms of radiation, such as light, sound or moving particles, for example, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which it passes.
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The Sun

Observation data
Mean distance
from Earth 1.4961011 m
(8.31 min at light speed)
Visual brightness (V) −26.74m [1]
Absolute magnitude 4.
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WATT

City of license Cadillac, Michigan
Broadcast area [1]
Branding NewsTalk 1240
First air date 1945
Frequency 1240 kHz
Format News-Talk-Sports
Power 1,000 watts
Class C
Owner MacDonald Garber Broadcasting
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