Intensity (physics)

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For other uses, see Intensity (disambiguation).

In physics, intensity is a measure of the time-averaged energy flux. 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. watt/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).

[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:

$P = \int I\, dA$

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. ( $A s u r f = 4π r 2$ 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 energy density of the wave is given by

$U = \frac{n^2 \epsilon_0}{2} |E|^2$ ,

and the intensity is obtained 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 $ε 0$ is the electric permittivity in vacuum.

[edit] Intensity in photometry and radiometry

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.

[edit] See also

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SI photometry units
Quantity	Symbol	SI unit	Abbr.	Notes
Luminous energy	Q_v	lumen second	lm·s	units are sometimes called talbots
Luminous flux	F	lumen (= cd·sr)	lm	also called luminous power
Luminous intensity	I_v	candela (= lm/sr)	cd	an SI base unit
Luminance	L_v	candela per square metre	cd/m²	units are sometimes called nits
Illuminance	E_v	lux (= lm/m²)	lx	Used for light incident on a surface
Luminous emittance	M_v	lux (= lm/m²)	lx	Used for light emitted from a surface
Luminous efficacy		lumen per watt	lm/W	ratio of luminous flux to radiant flux; maximum possible is 683.002 lm/W
SI • Photometry

[edit]

SI radiometry units
Quantity	Symbol	SI unit	Abbr.	Notes
Radiant energy	Q	joule	J	energy
Radiant flux	Φ	watt	W	radiant energy per unit time, also called radiant power
Radiant intensity	I	watt per steradian	W·sr⁻¹	power per unit solid angle
Radiance	L	watt per steradian per square metre	W·sr⁻¹·m⁻²	power per unit solid angle per unit projected source area. Sometimes confusingly called "intensity".
Irradiance	E, I	watt per square metre	W·m⁻²	power incident on a surface. Sometimes confusingly called "intensity".
Radiant exitance / Radiant emittance	M	watt per square metre	W·m⁻²	power emitted from a surface.
Radiosity	J or J_λ	watt per square metre	W·m⁻²	emitted plus reflected power leaving a surface
Spectral radiance	L_λ or L_ν	watt per steradian per metre³ or watt per steradian per square metre per hertz	W·sr⁻¹·m⁻³ or W·sr⁻¹·m⁻²·Hz⁻¹	commonly measured in W·sr⁻¹·m⁻²·nm⁻¹
Spectral irradiance	E_λ or E_ν	watt per metre³ or watt per square metre per hertz	W·m⁻³ or W·m⁻²·Hz⁻¹	commonly measured in W·m⁻²·nm⁻¹