# Intensity (physics)

Physical size
Surname intensity
Formula symbol ${\ displaystyle I}$
Size and
unit system
unit dimension
SI W · m -2 = kg · s -3 M · T −3

In physics, the intensity or radiation intensity is usually the surface power density when transporting energy . The term is also used for the amount of surface current density of other physical quantities. The term is mostly used for wave phenomena such as sound or electromagnetic radiation , but its definition also includes all other types of transport. For a given area in space, the intensity is calculated as the quotient of the quantity of the relevant variable (e.g. power) transferred through the area and the size of the area. The product of the spatial density (e.g. energy density ) and the speed of transport is equivalent .

Outside of physics, the term is also used in an imprecise way for “ strength ”, “ force ”, “ amplitude ” or “ level ”.

## Intensity in radiometry and photometry

In radio and photometry , the following quantities are referred to as "intensity" ("radiation intensity" or "light intensity"):

• Illuminance (photometric): the irradiance weighted with the sensitivity of the human eye ( photometric radiation equivalent ).

With "intensity", however - in deviation from the general definition of "intensity" mentioned in the introduction - the performance in relation to the solid angle can also be meant:

• Luminous intensity : the radiant intensity weighted with the photometric radiation equivalent.

In English, the terms radiant intensity and luminous intensity stand for the radiation intensity and the light intensity. Light intensity, on the other hand, is ambiguous.

## Intensity in wave theory

The intensity of electromagnetic radiation is the amount of the time mean ( ) of the Poynting vector${\ displaystyle \ textstyle \ langle \ dots \ rangle _ {t}}$ ${\ displaystyle \ textstyle S}$

${\ displaystyle I = | \ langle S \ rangle _ {t} |}$

In media without dispersion with the energy density , the relationship with the group speed applies as ${\ displaystyle \ textstyle W}$ ${\ displaystyle \ textstyle v _ {\ mathrm {gr}}}$

${\ displaystyle I = \ langle W \ rangle _ {t} \; v _ {\ mathrm {gr}} \,}$

The intensity is proportional to the square of the amplitude of the wave: ${\ displaystyle \ textstyle A}$

${\ displaystyle I \ propto A ^ {2} \,}$.

For a monochromatic, linearly polarized electromagnetic wave in a vacuum, the intensity is:

${\ displaystyle I = {\ frac {1} {2}} c \ varepsilon _ {0} E_ {0} ^ {2} = {\ frac {1} {2}} {\ frac {c} {\ mu _ {0}}} B_ {0} ^ {2} \ ,.}$

It is the speed of light , the electric field constant as well , and the maximum amplitude of the electric or magnetic field of the shaft. ${\ displaystyle \ textstyle c}$${\ displaystyle \ textstyle \ varepsilon _ {0}}$${\ displaystyle \ textstyle E_ {0}}$${\ displaystyle \ textstyle B_ {0}}$

In linear dielectric media with the refractive index, the following applies: ${\ displaystyle \ textstyle n}$

${\ displaystyle I = {\ frac {1} {2}} cn \ varepsilon _ {0} E_ {0} ^ {2} \,}$.

## Intensity of a point source

If a point source radiates the power in three dimensions and there is no loss of energy , then the intensity drops quadratically with the distance from the object: ${\ displaystyle \ textstyle P}$${\ displaystyle \ textstyle r}$

${\ displaystyle I = {\ frac {P} {4 \ pi r ^ {2}}} \,}$.

## Influence of a medium

When the medium dampens ( absorbs ), the wave loses energy, which is converted into heat energy, for example. If one assumes that the decrease in intensity is proportional to the intensity present at the respective location, an exponential curve results, analogous to the law of decay , the so-called Lambert-Beer law :

${\ displaystyle I (r) = I_ {0} \ cdot \ mathrm {e} ^ {- \ mu r} \ ,.}$

As the wave propagates in the medium , its intensity decreases exponentially. The absorption coefficient describes the material properties of the medium passed through. ${\ displaystyle \ mu}$