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[[Image:Refracción.png|thumb|Diagram showing displacement of the [[Sun]]'s image at sunrise and sunset]]

'''Atmospheric refraction''' is the deviation of [[light]] or other [[electromagnetic wave]] from a straight line as it passes through the [[atmosphere]] due to the variation in [[air]] density as a function of [[altitude]]. This refraction is due to the velocity of light through air decreasing (the [[Refractive index|index of refraction]] increases) with increased density. Atmospheric [[refraction]] near the ground produces [[mirage]]s and can make distant objects appear to shimmer or ripple, [[Looming and similar refraction phenomena|elevated or lowered, stretched or shortened]] with no mirage involved. The term also applies to the refraction of [[sound]].

Atmospheric refraction causes [[astronomical object]]s to appear higher in the sky than they are in reality. It affects not only lightrays but all electromagnetic radiation, although in varying degrees (see [[dispersion (optics)|dispersion in optics]]). For example in visible light, blue is more affected than red. This may cause astronomical objects to be spread out into a spectrum in high-resolution images.

Whenever possible, [[astronomer]]s will schedule their observations around the time of [[culmination]] of an object when it is highest in the sky. Likewise sailors will never shoot a star which is not at least 20° or more above the horizon. If observations close to the horizon cannot be avoided, it is possible to equip a [[telescope]] with control systems to compensate for the shift caused by the refraction. If the dispersion is a problem too, (in case of broadband high-resolution observations) atmospheric refraction correctors can be employed as well (made from pairs of rotating glass prisms). But as the amount of atmospheric refraction is a function of [[temperature]] and [[pressure]] as well as [[humidity]] (the amount of [[water vapor|water vapour]] is especially important at mid-infrared wavelengths) the amount of effort needed for a successful compensation can be prohibitive.

Atmospheric refraction becomes more severe when the atmospheric refraction is not homogenous, when there is turbulence in the air for example. This is the cause of [[scintillation (astronomy)|twinkling]] of the [[star]]s and deformation of the shape of the sun at sunset and sunrise.

==Values==
Atmospheric refraction of the light from a star is zero in the [[zenith]], less than 1′ (one [[arcminute|arc-minute]]) at 45° apparent [[celestial coordinate system|altitude]], and still only 5.3′ at 10° altitude; it quickly increases as altitude decreases, reaching 9.9′ at 5° altitude, 18.4′ at 2° altitude, and 35.4′ at the [[horizon]] ([[#CITEREFAllen1976|Allen 1976]], 125); all values are for 10 °C and 101.3 [[pascal (unit)|kPa]]
in the visible part of the spectrum.

On the horizon refraction is slightly greater than the apparent diameter of the Sun, so when the bottom of the sun's disc appears to touch the horizon, the sun's true altitude is negative. If the atmosphere suddenly vanished, the sun would too. By convention, [[sunrise]] and [[sunset]] refer to times at which the Sun’s upper limb appears on or disappears from the horizon and the standard value for the Sun’s true altitude is -51.4`: −35.4′ for the refraction and −16′ for the Sun’s [[semidiameter|semi-diameter]]. The altitude of a celestial body is normally given for the center of the body’s disc. In the case of the [[Moon]], additional corrections are needed for the Moon’s [[Parallax#Lunar_parallax|horizontal parallax]] and its apparent semi-diameter; both vary with the Earth–Moon distance.

Day-to-day variations in the weather will affect the exact times of sunrise and sunset ([[#CITEREFSchaeferLiller1990|Schaefer and Liller 1990]]) as well as moon-rise and moon-set, and for that reason it generally is not meaningful to give rise and set times to greater precision than the nearest minute ([[#CITEREFMeeus1991|Meeus 1991]], 103). More precise calculations can be useful for determining day-to-day changes in rise and set times that would occur with the standard value for refraction (for example [[#CITEREFMeeus2002|Meeus 2002]], 315) if it is understood that actual changes may differ because of unpredictable variations in refraction.

Because atmospheric refraction is 34′ on the horizon, but only 29′ at 0.5° above it, the setting or rising sun seems to be flattened by about 5′ (about 1/6 of its apparent diameter).

The light from distant objects on the earth is refracted too; the straight line from your eye to a distant mountain might be blocked by a closer hill, but the actual light path may curve enough to make the distant peak visible. A reasonable first guess: a mountain's apparent altitude at your eye (in degrees) will exceed its true altitude by its distance in kilometers divided by 1500. This assumes a fairly horizontal line of sight and ordinary air density; if the mountain is very high (so much of the sightline is in thinner air) divide by 1600 instead.

==Calculating refraction==
[[Image:BennettAtmRefractVsAlt.png|thumb|right|Plot of refraction vs. altitude using Bennett’s 1982 formula]]

Rigorous calculation of refraction requires numerical integration, using a method such as that of [[#CITEREFAuerStandish2000|Auer and Standish (2000)]]. [[#CITEREFBennett1982|Bennett (1982)]] developed a simple empirical formula for calculating refraction from the ''apparent'' altitude, using the algorithm of [[#CITEREFGarfinkel1967|Garfinkel (1967)]] as the reference; if ''h''<sub>a</sub> is the apparent altitude in degrees, refraction ''R'' in arcminutes is given by

:<math>R = \cot \left ( h_\mathrm{a} + \frac {7.31} {h_\mathrm{a} + 4.4} \right ) \,;</math>

the formula is accurate to within 0.07′ for the altitude range 0°–90° ([[#CITEREFMeeus1991|Meeus 1991]], 102). [[#CITEREFSæmundsson1986|Sæmundsson (1986)]] developed a formula for determining refraction from ''true'' altitude; if ''h'' is the true altitude in degrees, refraction ''R'' in arcminutes is given by

:<math>R = 1.02 \cot \left ( h + \frac {10.3} {h + 5.11} \right ) \,;</math>

the formula is consistent with Bennett’s to within 0.1′. Both formulas assume an [[atmospheric pressure]] of 101.0 kPa and a temperature of 10 °C; for different pressure ''P'' and temperature ''T'', refraction calculated from these formulas is multiplied by

:<math>\frac {P} {101} \, \frac {283} {273 + T} </math>

([[#CITEREFMeeus1991|Meeus 1991]], 103). Refraction increases approximately 1% for every 0.9 kPa increase in pressure, and decreases approximately 1% for every 0.9 kPa decrease in pressure. Similarly, refraction increases approximately 1% for every 3 °C decrease in temperature, and decreases approximately 1% for every 3 °C increase in temperature.

==Random refraction effects==
[[Image:Seeing Moon.gif|frame|right|An animated image of the [[Moon]]'s surface showing the effects of Earth's atmosphere on the view]]
[[Turbulence]] in the atmosphere magnifies and de-magnifies star images, making them appear brighter and fainter on a time-scale of milliseconds. The slowest components of these fluctuations are visible as twinkling (also called "scintillation").

Turbulence also causes small random motions of the star image, and produces rapid changes in its structure. These effects are not visible to the naked eye, but are easily seen even in small telescopes. They are called [[Astronomical seeing|"seeing"]] by astronomers.

==See also==
*[[Ibn al-Haytham]]
*[[Shen Kuo]]

==References==
* {{citation|ref="CITEREFAllen1976" | first1=C. W.|last1=Allen, C. W.|year=1976 |title=Astrophysical Quantities|edition=3rd ed. |publication-place=London|publisher=Athlone|isbn=0-485-11150-0}}
* {{citation | ref="CITEREFAuerStandish2000" | last1=Auer|first1=Lawrence H. |first2=E. Myles|last2=Standish|year= 2000 |bibcode=2000AJ....119.2472A |title=Astronomical Refraction: Computation for All Zenith Angles|journal=Astronomical Journal|volume=119|number=5 |pages=2472–2474.|doi = 10.1086/301325 }}
* {{citation | ref="CITEREFBennett1982" | last1=Bennett|first1=G.G.|year=1982|title=The Calculation of Astronomical Refraction in Marine Navigation|journal=Journal of Navigation|volume=35|pages=255–259| doi=10.1017/S0373463300022037 |bibcode=1982JNav...35..255B}}
* {{cite journal|first1=A. V. |last1=Filippenko|title=The importance of atmospheric differential refraction in spectrophotometry|year=1982|bibcode=1982PASP...94..715F|journal=Publ. Astron. Soc. Pac|pages=715–721|doi = 10.1086/131052 }}
* {{citation|ref="CITEREFGarfinkel1967" |last1=Garfinkel |first1=B. |year=1967 |bibcode=1967AJ.....72..235G |title=Astronomical Refraction in a Polytropic Atmosphere|journal=Astronomical Journal|volume=72|pages=235–254|doi = 10.1086/110225 }}
* {{wikicite | ref="CITEREFMeeus1991" | reference=Meeus, Jean. 1991. ''Astronomical Algorithms''. Richmond, Virginia: Willmann-Bell, Inc. ISBN 0-943396-35-2}}
* {{wikicite | ref="CITEREFMeeus2002" | reference=Meeus, Jean. 2002. ''More Mathematical Astronomy Morsels''. Richmond, Virginia: Willmann-Bell, Inc. ISBN 0-943396-74-3}}
* {{citation|first1=Brett D.|last1=Nener|first2=Neville|last2=Fowkes|first3=Laurent
|last3=Borredon|bibcode=2003JOSAA..20..867N|title=Analytical modesl of optical refraction in the troposphere|year=2003 |journal= J. Opt. Soc. Am.|volume=20|number=5|pages=867–875|doi = 10.1364/JOSAA.20.000867 }}
* {{citation | ref="CITEREFSæmundsson1986"| last1=Sæmundsson | first1=Þorsteinn |year=1986|title=Astronomical Refraction|journal=Sky and Telescope|volume=72 |pages=70|bibcode = 1986S&T....72...70S }}
* {{citation | ref="CITEREFSchaeferLiller1990" | last1=Schaefer|first1=Bradley E.|first2=William |last2=Liller|year= 1990|bibcode=1990PASP..102..796S |title=Refraction near the horizon|journal=Publications of the Astronomical Society of the Pacific|volume=102|pages=796–805|doi = 10.1086/132705 }}
*{{citation| first1=Michael E. |last1=Thomas|first2=Richard I.|last2=Joseph|title=Astronomical Refraction
|url=http://techdigest.jhuapl.edu/TD/td1703/thomas.pdf |year=1996|journal = Johns Hopkins Apl. Technical Digest
|pages=279–284|volume=17}}

==Further reading==
*{{Citation |last=Wang |first=Yu |date=20 March 1998 |title=Very High-Resolution Space Telescope Using the Earth Atmosphere as the Objective Lens |publisher=[[Jet Propulsion Laboratory]] |id={{hdl|2014/19082}} }}
* {{cite journal|last1=Hirt|first1=C.|last2=Guillaume|first2=S. |last3=Wisbar|first3=A.|
last4=Bürki|first4=B.|last5=Sternberg|first5=H.|
year=2010|title=Monitoring of the refraction coefficient of the lower atmosphere using a controlled set-up of simultaneous reciprocal vertical angle measurements|journal= Journal of Geophysical Research (JGR)|volume=115|pages=D21102|url=http://espace.library.curtin.edu.au:80/R?func=dbin-jump-full&local_base=gen01-era02&object_id=155357|accessdate=May 5, 2012|bibcode=2010JGRD..11521102H|doi = 10.1029/2010JD014067 }}

==External links==
*[http://mintaka.sdsu.edu/GF/explain/atmos_refr/astr_refr.html Astronomical Refraction]—Andrew T. Young
*[http://www.geocities.jp/taddy_frog/RefractionCorrection.java Java Programming1]
*[http://www.geocities.jp/taddy_frog/RefractionUncorrection.java Java Programming2]
*[http://www.geocities.jp/taddy_frog/AtmosphericRefraction.html JavaScript calculator]

[[Category:Observational astronomy]]
[[Category:Atmospheric and ocean optics]]

Fibrant object - Revision history

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