Intensity (physics)

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In physics, intensity is a measure of the energy flux, averaged over the period of the wave. The word "intensity" here is not synonymous with "strength", "amplitude", or "level", as it sometimes is in colloquial speech. For example, "the intensity of pressure" is meaningless, since the parameters of those variables do not match.

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. W/m²). It is possible to define the intensity of the water coming from a garden sprinkler, but intensity is used most frequently with waves (i.e. sound or light).

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[edit] Mathematical description

If a point source is radiating energy in three dimensions and there is no energy lost to the medium, then the intensity decreases in proportion to distance from the object squared. This is due to physics and geometry. Physically, conservation of energy applies. The consequence of this is that the net power coming from the source must be constant, thus:

P = \int I\, \cdot dA

where P is the net power radiated, I is the intensity as a function of position, and dA is a differential element of a closed surface that contains the source. That P is a constant. If we integrate over a surface of uniform intensity I, for instance over a sphere centered around a point source radiating equally in all directions, the equation becomes:

P = |I| \cdot A_{surf} = |I| \cdot 4\pi r^2 \,

where I is the intensity at the surface of the sphere, and r is the radius of the sphere. (A_{surf} = 4\pi r^2 is the expression for the surface area of a sphere). Solving for I, we get:

|I| = \frac{P}{A_{surf}} = \frac{P}{4\pi r^2}

If the medium is damped, then the intensity drops off more quickly than the above equation suggests.

Anything that can carry energy can have an intensity associated with it. For an electromagnetic wave, if E is the complex amplitude of the electric field, then the time-averaged energy density of the wave is given by

\left\langle U \right \rangle = \frac{n^2 \epsilon_0}{2} |E|^2 ,

and the intensity is obtained by multiplying this expression by the velocity of the wave, c/n:

I = \frac{c n \epsilon_0}{2} |E|^2,

where n is the refractive index, c is the speed of light in vacuum and \epsilon_0 is the vacuum permittivity.

The treatment above does not hold for electromagnetic fields that are not radiating, such as for an evanescent wave. In these cases, the intensity can be defined as the magnitude of the Poynting vector.[1]

[edit] Alternative definitions of "intensity"

In photometry and radiometry intensity has a different meaning: it is the luminous or radiant power per unit solid angle. This can cause confusion in optics, where intensity can mean any of radiant intensity, luminous intensity or irradiance, depending on the background of the person using the term. Radiance is also sometimes called intensity, especially by astronomers and astrophysicists, and in heat transfer.

[edit] See also

Table 1. SI photometry units
Quantity Symbol[nb 1] SI unit Symbol Dimension Notes
Luminous energy Qv [nb 2] lumen second lm⋅s T⋅J [nb 3] units are sometimes called talbots
Luminous flux Φv [nb 2] lumen (= cd⋅sr) lm J also called luminous power
Luminous intensity Iv candela (= lm/sr) cd J an SI base unit, luminous flux per unit solid angle
Luminance Lv candela per square metre cd/m2 L−2⋅J units are sometimes called nits
Illuminance Ev lux (= lm/m2) lx L−2⋅J used for light incident on a surface
Luminous emittance Mv lux (= lm/m2) lx L−2⋅J used for light emitted from a surface
Luminous exposure Hv lux second lx⋅s L−2⋅T⋅J
Luminous energy density ωv lumen second per metre3 lm⋅sm−3 L−3⋅T⋅J
Luminous efficacy η [nb 2] lumen per watt lm/W M−1⋅L−2⋅T3⋅J ratio of luminous flux to radiant flux
Luminous efficiency V 1 also called luminous coefficient
See also: SI · Photometry · Radiometry · (Compare)
  1. ^ Standards organizations recommend that photometric quantities be denoted with a suffix "v" (for "visual") to avoid confusion with radiometric or photon quantities.
  2. ^ a b c Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ or K for luminous efficacy.
  3. ^ "J" is the recommended symbol for the dimension of luminous intensity in the International System of Units.

Table 2. SI radiometry units
Quantity Symbol[nb 1] SI unit Symbol Dimension Notes
Radiant energy Qe[nb 2] joule J M⋅L2⋅T−2 energy
Radiant flux Φe[nb 2] watt W M⋅L2⋅T−3 radiant energy per unit time, also called radiant power.
Spectral power Φ[nb 2][nb 3] watt per metre W⋅m−1 M⋅L⋅T−3 radiant power per wavelength.
Radiant intensity Ie watt per steradian W⋅sr−1 M⋅L2⋅T−3 power per unit solid angle.
Spectral intensity I[nb 3] watt per steradian per metre W⋅sr−1⋅m−1 M⋅L⋅T−3 radiant intensity per wavelength.
Radiance Le watt per steradian per square metre W⋅sr−1m−2 M⋅T−3 power per unit solid angle per unit projected source area.

confusingly called "intensity" in some other fields of study.

Spectral radiance L[nb 3]
or
L[nb 4]
watt per steradian per metre3
or

watt per steradian per square
metre per hertz

W⋅sr−1m−3
or
W⋅sr−1⋅m−2Hz−1
M⋅L−1⋅T−3
or
M⋅T−2
commonly measured in W⋅sr−1⋅m−2⋅nm−1 with surface area and either wavelength or frequency.


Irradiance Ee[nb 2] watt per square metre W⋅m−2 M⋅T−3 power incident on a surface, also called radiant flux density.

sometimes confusingly called "intensity" as well.

Spectral irradiance E[nb 3]
or
E[nb 4]
watt per metre3
or
watt per square metre per hertz
W⋅m−3
or
W⋅m−2⋅Hz−1
M⋅L−1⋅T−3
or
M⋅T−2
commonly measured in W⋅m−2nm−1
or 10−22W⋅m−2⋅Hz−1, known as solar flux unit.[nb 5]


Radiant exitance /
Radiant emittance
Me[nb 2] watt per square metre W⋅m−2 M⋅T−3 power emitted from a surface.
Spectral radiant exitance /
Spectral radiant emittance
M[nb 3]
or
M[nb 4]
watt per metre3
or

watt per square
metre per hertz

W⋅m−3
or
W⋅m−2⋅Hz−1
M⋅L−1⋅T−3
or
M⋅T−2
power emitted from a surface per wavelength or frequency.


Radiosity Je or J[nb 3] watt per square metre W⋅m−2 M⋅T−3 emitted plus reflected power leaving a surface.
Radiant exposure He joule per square metre J⋅m−2 M⋅T−2
Radiant energy density ωe joule per metre3 J⋅m−3 M⋅L−1⋅T−2
See also: SI · Radiometry · Photometry · (Compare)
  1. ^ Standards organizations recommend that radiometric quantities should be denoted with a suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
  2. ^ a b c d e Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant emittance.
  3. ^ a b c d e f Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek) to indicate a spectral concentration. Spectral functions of wavelength are indicated by "(λ)" in parentheses instead, for example in spectral transmittance, reflectance and responsivity.
  4. ^ a b c Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek)—not to be confused with the suffix "v" (for "visual") indicating a photometric quantity.
  5. ^ NOAA / Space Weather Prediction Center includes a definition of the solar flux unit (SFU).

[edit] References

  1. ^ Paschotta, Rüdiger. "Optical Intensity". Encyclopedia of Laser Physics and Technology. RP Photonics. http://www.rp-photonics.com/optical_intensity.html. 
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