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== Black-body in the theory of diffraction ==
=== Macdonald's model ===
The concept of black-body was formulated initially for size of it to be much less than the wave length. To say about diffraction the method of [[geometrical optics]] is valid then. To apply the Plank law for emitting of black body one has to regard the restriction:
:<math> \lambda \ll\ L </math>,
where <math> L </math> is the characteristic size of object. In 20-th age, the series of attempts was taken to find approach that is valid for any wave length - similar to ideal reflecting surface. In that case, an according mathematical condition has to be formulated on surface of black-body.
<ref name="Zakhariev">{{cite book |last1=Zakhariev, Lev N., Lemanskii, Aleksander A. |first1=. |title=Scattering of Waves by 'Black' Bodies |date=1972 |publisher=Sovetskoje Radio, BBK: B343.132.0 [in Russian] |location=Moscow |pages=288}}</ref>
As to be known, [[Impedance matching|impedance matching]] is effective for the only [[angle of incidence]]. In 1911, Macdonald H.M. proposed nearly self-evident approach.
<ref>{{cite journal |last1=Macdonald |first1=Hector Muaro |title=The Effect Produced by an Obstacle on a Train of Electric Waves (A Perfectly Absorbing Obstacle) |journal=Philosophical Transactions of the Royal Society of London |date=1912 |volume=212 |issue=Series A |pages=484-496 |url=http://doi.org/10.1098/rsta1913.0010}}</ref> He used two well formulated problems in electrodynamics- that of reflection from ideal metal:
: <math> \mathbf E_{\tau} = 0 </math>,
and that of reflection from ideal magnetic:
: <math> \mathbf H_{\tau} = 0 </math>.
Half-sum of solutions is the field around the black-body in Macdonald's model. The approach is clear in the scope of the geometrical optics. Two reflected rays have equal amplitudes of opposite signs and cancel each other. Therefore, the convex surface does not reflect rays at all.
At the same time, surface forming convex and concave parts of surface allows double reflections. The second reflections have equal amplitudes of two rays what does not accord to black-body concept. Consequently, Macdonald's model is reasonable for the convex surface only. Diagrams of scattered
fields around black ball for Macdonald's model are calculated on the base of Maxwell's equations in monography <ref name="Zakhariev" />.
===Adjunct space===
Sommerfeld proposed to consider black flat screen as surface of continued space what is analogous to procedure in the theory of [[Argument|complex analysis]]. Therefore, the problem is got to be spacious instead of surface one.
<ref>{{cite journal |last1=Sommerfeld |first1=Arnold |title=Theoretishes über die Beugung der Röntgen Strahlen |journal=Zeitchrift für Mathematik und Physik- Wikisource |date=1901 |volume=Band 46 |pages=ss.11-97 |url=http://de.wikisource.org>wiki>Zeitschrift_für_Ma}}</ref>

The idea to continue physical space was developed later. In 1978, Sergei P. Efimov from [[Bauman Moscow State Technical University]] found that Macdonald's model is equivalent to that with symmetrical adjunct space.
<ref name="Efimov>{{cite journal |last1=Efimov |first1=Sergei P. |title=Absolutely black-body in diffraction theory |journal=Engineering and Electronic Physics |date=1978 |volume=23 |issue=Jan. |pages=6-13 |url=http://ui.adsabs.harvard.edu/abs/1978RaEI...23....7E}}</ref>
The spaces are connected formally on the surface of black-body. Actually, two problems are considered outside of the surface. One is with charges and currents, other is without that. Boundary conditions on the surface equate tangential components of electric and magnetic fields of two problems with changing sign of the magnetic component. In such a way, electric field in physical space is equal to half-sum of solutions of two problems for ideal reflecting surfaces:
:<math> \mathbf E= \frac{(\,\mathbf E_+ +\mathbf E_-)}{2} \qquad </math> (in physical space),
where <math> \mathbf E_+ </math> is field from problem for ideal metal and <math> \mathbf E_- </math> is the field from problem for ideal magnetic. In the adjunct space, where no charges and currents, the sought electric field is equal to the difference of the same fields:
:<math> \mathbf E= \frac{(\,\mathbf E_+ -\mathbf E_-)}{2} \qquad </math> (in adjunct space).
The concept of adjunct space proves that Macdonald's model is physically correct for all frequencies. The causality holds in the approach and considerations of scatter of wave packs is acceptable.
From symmetry of physical anf adjunct spaces follows two electrodynamical theorems:
* In state of the heat equilibrium, heat fluxes from surface in physical and adjunct spaces are equal to each other.
* Scattered field from thin black disc is equal to that from hole in flat thin screen (Babine's principle).
Macdonald's model and Efimov's consideration are valid for equations of acoustics, to equations of hydrodynamics, to diffusion equation. It should be noticed that half-sum of two subsidiary solutions is valid for linear equations only. It is clear that theoretical model needs a way for realizations.
<ref>{{cite journal |last1=Efimov |first1=Sergei P. |title=Compression of electromagnetic waves by anisotropic medium ('Non-reflecting crystal model') |journal=Radiophysics and Quantum Electronics |date=1978 |volume=21 |issue=9 |pages=916-920 |doi=10.1007/BF01031726 |url=https://www.link.springer.com/article/10.1007/BF01031726}}</ref>
<ref>{{cite journal |last1=Efimov |first1=Sergei P. |title=Compression of waves by artificial anisotropic medium |journal=Acoustical journal |date=1979 |volume=25 |issue=2 |pages=234-238 |url=http://www.akzh.ru_1979_ 234-238.pdf}}</ref>

The concept of adjunct space can be applied to the [[Black-hole|black hole]] in theory of [[General relativity| gravitation]]. The famous [[Schwarzschild metric]] looks mathematically simple:

:<math> \frac{\left (1-\frac{r_s}{4R}\right)^2}{\left (1+\frac{r_s}{4R}\right )^2}dt^2 + \left (1+\frac{r_s}{4R}\right)^2 (dx^2+dy^2+dz^2)</math>,
where <math>\mathbf R = (x,y,z) </math> is radius-vector, <math> r_s </math> is [[Schwarzschild metric|the Schwarzschild]] radius i.e. radius of black-hole.
From point of view of concept based on the adjunct space , it is useful to apply the following transformation of physical space:<ref name="Efimov"/>
:<math> \boldsymbol \rho = \frac{ a^2\mathbf R}{R^2} </math>,
where <math> a </math> is radius of sphere that adjunct space is attached to. Radius <math> a </math> is taken to give the Schwarzschild metrics again:
:<math> a =\frac{r^s}{4} </math>.
Therefore, the black hole can be considered as the connection of two symmetrical spaces on the surface of ball with radius <math> a </math>. In that case, well known peculiarity <math> R =0 </math> is disappeared.
===Black-body of arbitrary form===
[[Anechoic chamber|Non-reflecting chamber]] has absolutely absorbing walls. Regarding physical picture, adjunct space now is simply the surrounding space as far as the walls are missed. Therefore, adjunct spaces for the totally convex surface and concave one are identical. The adjunct space is continued along normal directed into side of convexity of surface. Details are described in the paper. <ref name="Efimov"/> The equivalent electrodynamical problem can be formulated on the base of boundary condition. It analogous to the impedance matching. Nevertheless, the boundary condition binds tangential components of electric and magnet fields not in the point but on all surface. The condition is based on [[Fourier optics|Stratton - Chu formula]].<ref>{{cite journal |last1=Stratton, J.A., Chu, L.J. |title=Diffraction Theory of Electromagnetic Waves |journal=Physical Review, Am. Phys. Soc. |date=1939-07-01 |volume=56 |issue=1 |pages=99-107
|doi=10.1103/physrev.56.99}}</ref><ref>{{cite book |last1=Jackson |first1=John David |title=Classical Electrodynamics |date=1999 |publisher=John Wiley&Sons Ltd.,OCLC 925677836 |isbn=0-471-30932-X |edition=3-th}}</ref>

To demonstrate approach, it is useful to deduce boundary condition for scalar problem when [[Helmholtz equation]] is valid. Fields on the surface are bound by [[Green's function]] in two points - <math>\mathbf x</math> and <math>\mathbf y </math>:
:<math> G(\mathbf {x,y}) = \frac{\exp (\mathbf {\mid x-y \mid})}{4 \pi (\mathbf {\mid x-y \mid}) }. </math>
Let be charges (or radiation sources) are placed in non-reflecting chamber i.e. in free space. Green's formula defines field <math> u(\mathbf x) </math> in adjunct space by boundary values on the surface of non-reflecting chamber. Upon sending argument <math>\mathbf x</math> on the surface, formula gives boundary condition:
:<math> \frac {u(\mathbf x)}{2}= \iint\limits_{S,\, y \neq x }\left[ { G(\mathbf{x,y})\frac { \partial u(\mathbf y)}{\partial n_y} -u(\mathbf y) \frac{\partial G(\mathbf{(x,y)} }{\partial n_y } }\right] \,dS_y .</math>
The [[surface integral|surface integral]] is calculated in the sense of [[Hadamard regularization]]. Normal <math> n_y </math> is directed outside of chamber i.e. in side of convexity of surface.

Boundary condition for convex black-body (for example ball) is the same. It is necessary however to take the normal directed outside of convex surface.

At last, boundary condition for arbitrary surface, containing convex and concave parts, conserves its form under condition that normal is directed into side of convexity. Therefore, the normal changes its sign on different parts of surface.
[[User:EfimovSP|EfimovSP]] ([[User talk:EfimovSP|talk]]) 18:57, 8 November 2020 (UTC)
{{reflist-talk}}

== Black hole absorbs all and reflects none ==

Would it be more accurate to say black holes redshift light travelling from close to their event horizon, since light passing close to the black hole can still curve back to the observer? A star collapsing into a black hole will seem to slow down and settle around its schwarzschild radius and effectively become redshifted until we cannot detect any light coming from its surface, though light arguably will get emitted from its surface just above the event horizon indefinitely as observed from a safe distance. Since this is not the main topic of this article, I am unsure whether such nitpicking is really necessary, nevertheless the fact that black holes emit radiation can be entirely derived without ever mentioning events on or past the horizon, while a classical black hole which absorbs all and reflects none would not emit thermal radiation. [[Special:Contributions/85.31.132.229|85.31.132.229]] ([[User talk:85.31.132.229|talk]]) 18:49, 2 December 2020 (UTC)


== What is it for? ==
== What is it for? ==
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The page for [[band emission]] could be easily slotted in to this article under Idealizations, though I don't know if there's enough there to warrant its own subheading or if it could be added under a heading like: <b>Band emissions</b> with justification of why measuring the emissions over a specific spectral band is useful. [[User:Reconrabbit|Reconrabbit]] ([[User talk:Reconrabbit|talk]]) 19:02, 11 December 2023 (UTC)
The page for [[band emission]] could be easily slotted in to this article under Idealizations, though I don't know if there's enough there to warrant its own subheading or if it could be added under a heading like: <b>Band emissions</b> with justification of why measuring the emissions over a specific spectral band is useful. [[User:Reconrabbit|Reconrabbit]] ([[User talk:Reconrabbit|talk]]) 19:02, 11 December 2023 (UTC)

== Black body absorption and emission? Which is king? ==

I am trying to understand black bodies (bb), not being a physicist. This article, like others I have read, talks about absorption and emissions of radiation. Absorption by a bb is defined to be 100% of incident radiation. In the next sentence, at the beginning, we are told that a bb emits radiation. Confusingly, that suggests that absorption is not 100%; some is going back out. Emission qualities depend on the temperature. Is the temperature determined by the absorbed radiation? Or just by an independent local heat source? Is the thermal capacity of the bb relevant to heating caused by absorbed radiation? Is the relevance of a bb to physics because it absorbs, it emits, or both? Or is it because it transforms incident radiation into outgoing radiation with different properties dependent on its temperature which is determined by what?? Any clarifications would be appreciated. [[User:KPD674|KPD674]] ([[User talk:KPD674|talk]]) 11:35, 17 August 2024 (UTC)

Latest revision as of 12:26, 17 August 2024

Former good article nomineeBlack body was a good articles nominee, but did not meet the good article criteria at the time. There may be suggestions below for improving the article. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.
Article milestones
DateProcessResult
July 21, 2006Good article nomineeNot listed


What is it for?

[edit]

The article starts out with "A black body or blackbody is an idealized physical body...". At that point it should say why anyone would want to idealize a body and here should be examples of what a "body" is. I'm not expert enough to add it myself, but something along the lines of "... that is used as a stand-in for actual physical objects, such as planets and humans, in order to simplify the math required to model them."

Math error?

[edit]

At the time of writing this comment, the Black Holes section has a formula that drops the following error (in the Brave browser, running on macOS Big Sur): 

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle T=\frac {\hbar c^3}{8\pi Gk_\text{B}M} \ ,}

I'm not familiar enough with MathML or the <math> tag to be of any help, and my only hope is that someone who follows this page (or has it on their watchlist) is able to check it and correct the error.

Feel free to remove this message once the issue is fixed. — Gwyneth Llewelyn (talk) 19:17, 6 March 2023 (UTC)[reply]

Space to include band emission

[edit]

The page for band emission could be easily slotted in to this article under Idealizations, though I don't know if there's enough there to warrant its own subheading or if it could be added under a heading like: Band emissions with justification of why measuring the emissions over a specific spectral band is useful. Reconrabbit (talk) 19:02, 11 December 2023 (UTC)[reply]

Black body absorption and emission? Which is king?

[edit]

I am trying to understand black bodies (bb), not being a physicist. This article, like others I have read, talks about absorption and emissions of radiation. Absorption by a bb is defined to be 100% of incident radiation. In the next sentence, at the beginning, we are told that a bb emits radiation. Confusingly, that suggests that absorption is not 100%; some is going back out. Emission qualities depend on the temperature. Is the temperature determined by the absorbed radiation? Or just by an independent local heat source? Is the thermal capacity of the bb relevant to heating caused by absorbed radiation? Is the relevance of a bb to physics because it absorbs, it emits, or both? Or is it because it transforms incident radiation into outgoing radiation with different properties dependent on its temperature which is determined by what?? Any clarifications would be appreciated. KPD674 (talk) 11:35, 17 August 2024 (UTC)[reply]

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