Editing Irradiance (section)

= \frac{n \varepsilon_0 c}{2} E_\mathrm{m}^2 \cos \alpha =
 \frac{n }{2Z_0} E_\mathrm{m}^2 \cos \alpha,</math>
where
*''E''<sub>m</sub> is the amplitude of the wave's electric field;
*''n'' is the [[refractive index]] of the medium of propagation;
*''c'' is the [[speed of light]] in [[vacuum]];

* μ<sub>0</sub> is the [[vacuum permeability]];

*ε<sub>0</sub> is the [[vacuum permittivity]];
**<math display="inline">c={\frac {1}{\sqrt {\varepsilon_0 \mu_0 }}}</math>
**<math display="inline">Z_0=\mu_0c</math> is the [[impedance of free space]].

This formula assumes that the [[magnetic susceptibility]] is negligible; i.e. that ''μ''<sub>r</sub> ≈ 1 (''μ'' ≈ μ<sub>0</sub>) where ''μ''<sub>r</sub> is the relative [[magnetic permeability]] of the propagation medium. This assumption is typically valid in transparent media in the [[visible spectrum|optical frequency range]].

==Point source==
A [[point source]] of light produces spherical wavefronts. The irradiance in this case varies inversely with the square of the distance from the source.
:<math>
E = \frac P A = \frac P {4 \pi r^2},
</math>
where
*{{mvar|r}} is the distance;
*{{mvar|P}} is the [[radiant flux]];
*{{mvar|A}} is the surface area of a sphere of radius {{mvar|r}}.

For quick approximations, this equation indicates that doubling the distance reduces irradiation to one quarter; or similarly, to double irradiation, reduce the distance to 71%.

In astronomy, stars are routinely treated as point sources even though they are much larger than the Earth. This is a good approximation because the distance from even a nearby star to the Earth is much larger than the star's diameter. For instance, the irradiance of [[Alpha Centauri A]] (radiant flux: 1.5 [[Solar luminosity|L<sub>☉</sub>]], distance: 4.34 [[light-year|ly]]) is about 2.7 × 10<sup>−8</sup> W/m<sup>2</sup> on Earth.

==Solar irradiance==
{{main|Solar irradiance}}
The global irradiance on a horizontal surface on Earth consists of the direct irradiance ''E''<sub>e,dir</sub> and diffuse irradiance ''E''<sub>e,diff</sub>. On a tilted plane, there is another irradiance component, ''E''<sub>e,refl</sub>, which is the component that is reflected from the ground. The average ground reflection is about 20% of the global irradiance. Hence, the irradiance ''E''<sub>e</sub> on a tilted plane consists of three components:<ref name=Quaschning>{{cite journal |last=Quaschning |first=Volker |author-link=Volker Quaschning |title=Technology fundamentals—The sun as an energy resource |journal=Renewable Energy World |volume=6 |date=2003 |issue=5 |pages=90–93 |url=https://www.volker-quaschning.de/articles/fundamentals1/index_e.html}}</ref>
:<math>E_\mathrm{e} = E_{\mathrm{e},\mathrm{dir}} + E_{\mathrm{e},\mathrm{diff}} + E_{\mathrm{e},\mathrm{refl}}.</math>

The [[integral]] of solar irradiance over a time period is called "[[Radiant exposure|solar exposure]]" or "[[insolation]]".<ref name=Quaschning/><ref>{{Cite journal | last1 = Liu | first1 = B. Y. H. | last2 = Jordan | first2 = R. C. | doi = 10.1016/0038-092X(60)90062-1 | title = The interrelationship and characteristic distribution of direct, diffuse and total solar radiation | journal = Solar Energy | volume = 4 | issue = 3 | pages = 1 | year = 1960 |bibcode = 1960SoEn....4....1L }}</ref>

Average solar irradiance at the top of the Earth's atmosphere is roughly 1361 W/m<sup>2</sup>, but at surface irradiance is approximately 1000 W/m<sup>2</sup> on a clear day.

==SI radiometry units==
{{SI radiometry units}}
[[File:photometry_radiometry_units.svg|thumb|upright=1.5|Comparison of photometric and radiometric quantities]]

==See also==
{{Div col|small=yes}}
*[[Albedo]]
*[[Fluence]]
*[[Illuminance]]
*[[Insolation]]
*[[Light diffusion]]
*[[PI curve]] (photosynthesis-irradiance curve)
*[[Solar azimuth angle]]
*[[Solar irradiance]]
*[[Solar noon]]
*[[Spectral flux density]]
*[[Stefan–Boltzmann law]]
{{Div col end}}

==References==
{{Reflist}}

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[[Category:Physical quantities]]
[[Category:Radiometry]]