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பின்னர் ஃபிரெனெல்லின் இழுப்புக் கெழு, சார்பியல் கோட்பாட்டின் படி வேகத்தை கணக்கிடும் சமன்பாட்டுடன் சேர்க்கப்பட்டது.
== சோதனையின் தொடர்ச்சி ==
== Repetitions ==
[[File:MM86-5.png|300px|thumb|1886 ஆம் ஆண்டு மைக்கேல்சன்-மோர்லியால் மேம்படுத்தப்பட்ட பியாசோ சோதனை. '''''a''''' என்ற ஒளி மூலத்திலிருந்து வெளிவரும் இணைகற்றையாக்கப்பட்ட ஒளி, '''''b''''' என்ற கற்றைப் பிரிப்பானால் பிரிக்கப்பட்டு '''''b c d e f b g''''' என்ற பாதையிலும், '''''b f e d c b g''''' என்ற பாதையிலும் பிரிகிறது.]]
[[File:MM86-5.png|300px|thumb|Improved Fizeau type experiment by Michelson and Morley in 1886. Collimated light from source '''''a''''' falls on beam splitter '''''b''''' where it divides: one part follows the path '''''b c d e f b g''''' and the other the path '''''b f e d c b g'''''.]]
[[Albert A. Michelson]] and [[Edward W. Morley]] (1886)<ref name=mich group=P /> repeated Fizeau's experiment with improved accuracy, addressing several concerns with Fizeau's original experiment: (1) Deformation of the optical components in Fizeau's apparatus could cause artifactual fringe displacement; (2) observations were rushed, since the pressurized flow of water lasted only a short time; (3) the [[laminar flow]] profile of water flowing through Fizeau's small diameter tubes meant that only their central portions were available, resulting in faint fringes; (4) there were uncertainties in Fizeau's determination of flow rate across the diameter of the tubes. Michelson redesigned Fizeau's apparatus with larger diameter tubes and a large reservoir providing three minutes of steady water flow. His [[common path interferometer]] design provided automatic compensation of path length, so that white light fringes were visible at once as soon as the optical elements were aligned. Topologically, the light path was that of a [[Common path interferometer#Sagnac|Sagnac interferometer]] with an even number of reflections in each light path.<ref name=Hariharan2007 group=S/> This offered extremely stable fringes that were, to first order, completely insensitive to any movement of its optical components. The stability was such that it was possible for him to insert a glass plate at '''''h''''' or even to hold a lighted match in the light path without displacing the center of the fringe system. Using this apparatus, Michelson and Morley were able to completely confirm Fizeau's results.<ref name=mich group=P /> ▼1886 ஆம் ஆண்டு [[ஆல்பர்ட் ஆபிரகாம் மைக்கல்சன்| மைக்கல்சன்]] மற்றும் மோர்லி இணைந்து பியாசோவின் சோதனையை மேம்படுத்தினர். தங்கள் [[மைக்கல்சன்-மோர்லி பரிசோதனை]]யின் மூலம் பல முடிவுகளைப் பெற்றனர்.<ref name=mich group=P />
▲[[Albert A. Michelson]] and [[Edward W. Morley]] (1886)<ref name=mich group=P /> repeated Fizeau's experiment with improved accuracy, addressing several concerns with Fizeau's original experiment: (1) Deformation of the optical components in Fizeau's apparatus could cause artifactual fringe displacement; (2) observations were rushed, since the pressurized flow of water lasted only a short time; (3) the [[laminar flow]] profile of water flowing through Fizeau's small diameter tubes meant that only their central portions were available, resulting in faint fringes; (4) there were uncertainties in Fizeau's determination of flow rate across the diameter of the tubes. Michelson redesigned Fizeau's apparatus with larger diameter tubes and a large reservoir providing three minutes of steady water flow. His [[common path interferometer]] design provided automatic compensation of path length, so that white light fringes were visible at once as soon as the optical elements were aligned. Topologically, the light path was that of a [[Common path interferometer#Sagnac|Sagnac interferometer]] with an even number of reflections in each light path.<ref name=Hariharan2007 group=S/> This offered extremely stable fringes that were, to first order, completely insensitive to any movement of its optical components. The stability was such that it was possible for him to insert a glass plate at '''''h''''' or even to hold a lighted match in the light path without displacing the center of the fringe system. Using this apparatus, Michelson and Morley were able to completely confirm Fizeau's results.<ref name=mich group=P />
Other experiments were conducted by [[Pieter Zeeman]] in 1914–1915. Using a scaled-up version of Michelson's apparatus connected directly to [[Amsterdam]]'s main water conduit, Zeeman was able to perform extended measurements using monochromatic light ranging from violet (4358 Å) through red (6870 Å) to confirm Lorentz's modified coefficient.<ref name=zee1 group=P /><ref name=zee2 group=P />
Since then, many experiments have been conducted measuring such dragging coefficients, often in combination with the Sagnac effect.<ref group=S name=sted /> For instance, in experiments using [[ring laser]]s together with rotating disks,<ref group=P name=macek /><ref group=P name=bilger1 /><ref group=P name=bilger2 /><ref group=P name=sanders /> or in [[Neutron interferometer|neutron interferometric]] experiments.<ref group=P name=klein /><ref group=P name=bonse /><ref group=P name=arif /> Also a transverse dragging effect was observed, i.e. when the medium is moving at right angles to the direction of the incident light.<ref group=P name=jones1 /><ref group=P name=jones2 />
== Hoek experiment ==
An indirect confirmation of Fresnel's dragging coefficient was provided by [[Martin Hoek]] (1868).<ref group=P name=hoek /><ref group=S name=ferr />
His apparatus was similar to Fizeau's, though in his version only one arm contained an area filled with resting water, while the other arm was in the air. As seen by an observer resting in the aether, Earth and hence the water is in motion. So the following travel times of two light rays traveling in opposite directions were calculated by Hoek (neglecting the transverse direction, see image):
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<math>t_{1}=\frac{AB}{c+v}+\frac{DE}{\frac{c}{n}-v} \ ,</math>
<math>t_{2}=\frac{AB}{c-v}+\frac{DE}{\frac{c}{n}+v} \ .</math>
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[[File:HoekExperiment with expected results.png|600px|thumb|Hoek expected the observed spectrum to be continuous with the apparatus oriented transversely to the aether wind, and to be banded with the apparatus oriented parallel to the wind. In the actual experiment, he observed no banding regardless of the instrument's orientation.]]
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The travel times are not the same, which should be indicated by an interference shift. However, if Fresnel's dragging coefficient is applied to the water in the aether frame, the travel time difference (to first order in ''v/c'') vanishes. Using different setups Hoek actually obtained a null result, confirming Fresnel's dragging coefficient. (For a similar experiment refuting the possibility of ''shielding'' the aether wind, see [[Hammar experiment]]).
In the particular version of the experiment shown here, Hoek used a prism ''P'' to disperse light from a slit into a spectrum which passed through a collimator ''C'' before entering the apparatus. With the apparatus oriented parallel to the hypothetical aether wind, Hoek expected the light in one circuit to be retarded 7/600 mm with respect to the other. Where this retardation represented an integral number of wavelengths, he expected to see constructive interference; where this retardation represented a half-integral number of wavelengths, he expected to see destructive interference. In the absence of dragging, his expectation was for the observed spectrum to be continuous with the apparatus oriented transversely to the aether wind, and to be banded with the apparatus oriented parallel to the aether wind. His actual experimental results were completely negative.<ref group=P name=hoek /><ref group=S name=ferr />
==Controversy==
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