Angular diameter distance - Revision history

en>CommonsDelinker: Replacing Distanza_di_diametro_angolare.gif with File:Distanza_di_diametro_angolare.png (by GifTagger because: Replacing GIF by exact PNG duplicate.).

2015-01-04T17:04:25Z

Replacing Distanza_di_diametro_angolare.gif with File:Distanza_di_diametro_angolare.png (by GifTagger because: Replacing GIF by exact PNG duplicate.).

← Older revision		Revision as of 19:04, 4 January 2015
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	~~{{Distinguish\|Cauchy~~'~~s functional equation}}~~		Jayson Berryhill is how I'm called and my wife doesn't like it at all. My working day job is an info officer but I've already utilized good psychic ([http://srncomm.com/blog/2014/08/25/relieve-that-stress-find-a-new-hobby/ srncomm.com]) for an additional one. Her family lives in Alaska but her husband desires them to transfer. As a woman what she truly likes is fashion and she's been performing it for quite [http://www.herandkingscounty.com/content/information-and-facts-you-must-know-about-hobbies psychic love readings] a while.<br><br>Review my web site :: online psychic ([http://www.article-galaxy.com/profile.php?a=143251 mouse click the following web page])

	~~[[Image:Cauchy-equation-1.svg\|thumb\|Refractive index vs. wavelength for [[BK7 glass]]. Red crosses show measured values. Over the visible region (red shading), Cauchy~~'~~s equation (blue line) agrees well with the measured refractive indices and the Sellmeier plot (green dashed line)~~. ~~It deviates in the ultraviolet and infrared regions.]]~~

	~~'''Cauchy's equation'''~~ is an ~~[[empirical relationship]] between the [[refractive index]] and [[wavelength]] of light for a particular [[transparency~~ (~~optics)\|transparent]] material. It is named for the mathematician~~ [~~[Augustin-Louis Cauchy]], who defined it in 1836.~~

	~~==The equation==~~
	~~The most general form of Cauchy's equation is~~

	:~~<math> n(\lambda) = B + \frac {C}{\lambda^2} + \frac{D}{\lambda^4} + \cdots,<~~/~~math>~~

	~~where ''n'' is the refractive index, λ is the wavelength, ''B'', ''C'', ''D'', etc~~.~~, are [[coefficient]]s~~ that ~~can be determined for~~ a ~~material by fitting the equation to measured refractive indices at known wavelengths~~. ~~The coefficients are usually quoted~~ for ~~λ as the [[vacuum wavelength]]~~ in ~~[[micrometre]]s~~.

	~~Usually, it~~ is ~~sufficient to use a two-term form of the equation:~~

	~~:<math> n(\lambda) = B + \frac{C}{\lambda^2},</math>~~

	~~where the coefficients ''B''~~ and '~~'C'' are determined specifically~~ for ~~this form of the equation.~~

	~~A table of coefficients for common optical materials is shown below~~:

	~~{\| border="1" cellspacing="0" cellpadding="4"~~
	~~\|'''Material''' \|\| '''B''' \|\| '''C''' (μm<sup>2<~~/~~sup>)~~
	\|-
	~~\|Fused silica \|\| 1~~.~~4580 \|\| 0~~.~~00354~~
	\|-
	~~\|Borosilicate glass BK7 \|\| 1.5046 \|\| 0.00420~~
	\|-
	~~\|Hard crown glass K5 \|\| 1.5220 \|\| 0.00459~~
	\|-
	~~\|Barium crown glass BaK4 \|\| 1.5690 \|\| 0.00531~~
	\|-
	~~\|Barium flint glass BaF10 \|\| 1.6700 \|\| 0.00743~~
	\|-
	~~\|Dense flint glass SF10 \|\| 1.7280 \|\| 0.01342~~
	\|}

	~~The theory of light~~-~~matter interaction on which Cauchy based this equation was later found to be incorrect~~. ~~In particular, the equation is only valid for regions of normal [[dispersion~~ (~~optics)\|dispersion]] in the~~ [~~[visible]] wavelength region~~. ~~In the [[infrared]], the equation becomes inaccurate, and it cannot represent regions of anomalous dispersion~~. ~~Despite this, its mathematical simplicity makes it useful in some applications~~.

	~~The [[Sellmeier equation]] is~~ a ~~later development of Cauchy's work that handles anomalously dispersive regions, and more accurately models a material's refractive index across~~ the ~~[[ultraviolet~~]~~], visible, and infrared spectrum.~~

	~~==References==~~
	*F.A. Jenkins and H.E. White, ''Fundamentals of Optics'', 4th ed., McGraw-Hill, Inc. (1981).

	~~==See also==~~
	*[[Sellmeier equation]]

	~~[[Category:Optics]]~~
	~~[[Category:Equations]]~~

en>OgreBot: replacing File:Angular diameter distance.gif with commons equivalent File:Distanza di diametro angolare.gif (report errors here)

2013-09-13T05:01:17Z

replacing File:Angular diameter distance.gif with commons equivalent File:Distanza di diametro angolare.gif (report errors here)

← Older revision		Revision as of 07:01, 13 September 2013
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	~~Hi there~~. ~~My name~~ is ~~Sophia Meagher although it~~ is ~~not~~ the ~~name on my birth certification~~. The ~~favorite pastime for him and his children~~ is ~~to perform lacross and he~~'ll be ~~starting something else alongside with it~~. ~~Invoicing is what I do~~. ~~Ohio~~ is ~~exactly~~ where ~~his home is~~ and ~~his family enjoys it~~.<br><br>~~Also visit my web~~-~~site~~ ... [~~http://Www~~.~~chk~~.~~woobi~~.co.~~kr/xe/?document_srl~~=~~346069 phone psychic readings~~]		{{Distinguish\|Cauchy's functional equation}}

			[[Image:Cauchy-equation-1.svg\|thumb\|Refractive index vs. wavelength for [[BK7 glass]]. Red crosses show measured values. Over the visible region (red shading), Cauchy's equation (blue line) agrees well with the measured refractive indices and the Sellmeier plot (green dashed line). It deviates in the ultraviolet and infrared regions.]]

			'''Cauchy's equation''' is an [[empirical relationship]] between the [[refractive index]] and [[wavelength]] of light for a particular [[transparency (optics)\|transparent]] material. It is named for the mathematician [[Augustin-Louis Cauchy]], who defined it in 1836.

			==The equation==
			The most general form of Cauchy's equation is

			:<math> n(\lambda) = B + \frac {C}{\lambda^2} + \frac{D}{\lambda^4} + \cdots,</math>

			where ''n'' is the refractive index, λ is the wavelength, ''B'', ''C'', ''D'', etc., are [[coefficient]]s that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths. The coefficients are usually quoted for λ as the [[vacuum wavelength]] in [[micrometre]]s.

			Usually, it is sufficient to use a two-term form of the equation:

			:<math> n(\lambda) = B + \frac{C}{\lambda^2},</math>

			where the coefficients ''B'' and ''C'' are determined specifically for this form of the equation.

			A table of coefficients for common optical materials is shown below:

			{\| border="1" cellspacing="0" cellpadding="4"
			\|'''Material''' \|\| '''B''' \|\| '''C''' (μm<sup>2</sup>)
			\|-
			\|Fused silica \|\| 1.4580 \|\| 0.00354
			\|-
			\|Borosilicate glass BK7 \|\| 1.5046 \|\| 0.00420
			\|-
			\|Hard crown glass K5 \|\| 1.5220 \|\| 0.00459
			\|-
			\|Barium crown glass BaK4 \|\| 1.5690 \|\| 0.00531
			\|-
			\|Barium flint glass BaF10 \|\| 1.6700 \|\| 0.00743
			\|-
			\|Dense flint glass SF10 \|\| 1.7280 \|\| 0.01342
			\|}

			The theory of light-matter interaction on which Cauchy based this equation was later found to be incorrect. In particular, the equation is only valid for regions of normal [[dispersion (optics)\|dispersion]] in the [[visible]] wavelength region. In the [[infrared]], the equation becomes inaccurate, and it cannot represent regions of anomalous dispersion. Despite this, its mathematical simplicity makes it useful in some applications.

			The [[Sellmeier equation]] is a later development of Cauchy's work that handles anomalously dispersive regions, and more accurately models a material's refractive index across the [[ultraviolet]], visible, and infrared spectrum.

			==References==
			*F.A. Jenkins and H.E. White, ''Fundamentals of Optics'', 4th ed., McGraw-Hill, Inc. (1981).

			==See also==
			*[[Sellmeier equation]]

			[[Category:Optics]]
			[[Category:Equations]]

en>RedBot: r2.5.2) (Robot: Adding zh:角直徑距離

2012-02-21T18:16:00Z

r2.5.2) (Robot: Adding zh:角直徑距離

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