Euler–Mascheroni constant: Difference between revisions

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[[File:Foucault apparatus.JPG|thumb|300px|Figure 1: Schematic of the Foucault apparatus. ''Left panel'': Light is reflected by a rotating mirror (left) toward a stationary mirror (top). ''Right panel'': The reflected light from the stationary mirror bounces from the rotating mirror that has advanced an angle θ during the transit of the light. The telescope at an angle 2θ from the source picks up the reflected beam from the rotating mirror.]]
[[File:Fizeau.JPG|thumb|300px|Figure 2: Schematic of the Fizeau apparatus. The light passes on one side of a tooth on the way out, and the other side on the way back, assuming the cog rotates one tooth during transit of the light.]]


The '''Fizeau–Foucault apparatus''' (1850) (Figure 1) was designed by the [[France|French]] [[physics|physicists]] [[Hippolyte Fizeau]] and [[Léon Foucault]] for measuring the [[speed of light]]. The apparatus involves [[light]] reflecting off a [[rotation|rotating]] [[mirror]], toward a stationary mirror some 20 miles (35 kilometers) away. As the rotating mirror will have moved slightly in the time it takes for the light to bounce off the stationary mirror (and return to the rotating mirror), it will thus be deflected away from the original source, by a small angle.<ref name=Baierlein>
{{cite book 
|title=Newton to Einstein: the trail of light : an excursion to the wave-particle duality and the special theory of relativity
|author=Ralph Baierlein
|page=44; Figure 2.6 and discussion
|url=http://books.google.com/books?id=wrmZrcE0fPMC&pg=PA44
|isbn=0-521-42323-6
|year=2001
|publisher=Cambridge University Press }}
</ref> If the distance between mirrors is ''h'', the time between the first and second reflections on the rotating mirror is 2''h''/''c'' (''c'' = speed of light). If the mirror rotates at a known constant angular rate <math>\omega</math>, the angle ''θ'' is swept in the same time as the light roundtrip, so:


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:<math>\frac{\theta}{\omega} =  \frac {2h}{c}=t \ .  </math>
 
In other words the speed of light is calculated from the observed angle ''θ'', known angular speed and measured distance ''h'' as
 
:<math>c = \frac {2 \omega h}{\theta } \ . </math>
 
The detector is at an angle 2''θ'' from the source direction because the normal to the rotating mirror rotates by ''θ'', decreasing by ''θ'' both the angle of incidence of the beam and its angle of reflection.
 
Foucault based his apparatus on an earlier experiment by Fizeau (Figure 2) who, in 1849, used two fixed mirrors, one partially obscured by a rotating cogwheel.<ref name=Al-Azzawi>{{cite book |title=Photonics: principles and practices |author=Abdul Al-Azzawi |url=http://books.google.com/books?id=H3dtlDZrfwkC&pg=PA9 |page=9 |isbn=0-8493-8290-4 |year=2006 |publisher=CRC Press}}</ref>  Fizeau's value for light's speed was about 5% too high. 
 
The Fizeau experiment to measure the [[speed of light]] in water has been viewed as "driving the last nail in the coffin" of [[Isaac Newton|Newton]]'s [[Corpuscular theory of light|corpuscle theory of light]] when it showed that light travels more slowly through water than through air.<ref>{{cite book | title = Understanding Physics | author = David Cassidy, Gerald Holton, James Rutherford | publisher = Birkhäuser | year = 2002 | isbn = 0-387-98756-8 | url = http://books.google.com/books?id=rpQo7f9F1xUC&pg=PA382&dq=Foucault+speed-of-light+wave+theory}}</ref> Newton predicted refraction as a ''pull'' of the medium upon the light, implying an increased speed of light in the medium. However, Fizeau showed the speed of light in water to be ''less'' than in air, not more, by inserting a tube of water in the light path.<ref name=Walker>{{cite book |title=Optical Engineering Fundamentals |url=http://books.google.com/books?id=Ccx9OM7iph8C&pg=PA13 |page=13 |author=Bruce H Walker |isbn=0-8194-2764-0 |publisher=SPIE Press |year=1998}}</ref>
 
==References==
{{Reflist}}
 
==External links==
* [http://imgbase-scd-ulp.u-strasbg.fr/displayimage.php?album=648&pos=24 Diagram] showing the original experimental design found in the second volume of Foucalt's collected works: [http://num-scd-ulp.u-strasbg.fr:8080/527/ Volume Two - ''Recueil des travaux scientifiques de Léon Foucault''] 1878.
* [http://www.pas.rochester.edu/~pavone/particle-www/teachers/demonstrations/FoucaultDemonstration.htm Speed of Light (The Foucault Method)]
* [http://www.st-andrews.ac.uk/~ulf/media.html Light in moving media]
 
{{DEFAULTSORT:Fizeau-Foucault apparatus}}
[[Category:Optical metrology]]
[[Category:Physics experiments]]

Revision as of 01:46, 21 January 2014

Figure 1: Schematic of the Foucault apparatus. Left panel: Light is reflected by a rotating mirror (left) toward a stationary mirror (top). Right panel: The reflected light from the stationary mirror bounces from the rotating mirror that has advanced an angle θ during the transit of the light. The telescope at an angle 2θ from the source picks up the reflected beam from the rotating mirror.
Figure 2: Schematic of the Fizeau apparatus. The light passes on one side of a tooth on the way out, and the other side on the way back, assuming the cog rotates one tooth during transit of the light.

The Fizeau–Foucault apparatus (1850) (Figure 1) was designed by the French physicists Hippolyte Fizeau and Léon Foucault for measuring the speed of light. The apparatus involves light reflecting off a rotating mirror, toward a stationary mirror some 20 miles (35 kilometers) away. As the rotating mirror will have moved slightly in the time it takes for the light to bounce off the stationary mirror (and return to the rotating mirror), it will thus be deflected away from the original source, by a small angle.[1] If the distance between mirrors is h, the time between the first and second reflections on the rotating mirror is 2h/c (c = speed of light). If the mirror rotates at a known constant angular rate , the angle θ is swept in the same time as the light roundtrip, so:

In other words the speed of light is calculated from the observed angle θ, known angular speed and measured distance h as

The detector is at an angle 2θ from the source direction because the normal to the rotating mirror rotates by θ, decreasing by θ both the angle of incidence of the beam and its angle of reflection.

Foucault based his apparatus on an earlier experiment by Fizeau (Figure 2) who, in 1849, used two fixed mirrors, one partially obscured by a rotating cogwheel.[2] Fizeau's value for light's speed was about 5% too high.

The Fizeau experiment to measure the speed of light in water has been viewed as "driving the last nail in the coffin" of Newton's corpuscle theory of light when it showed that light travels more slowly through water than through air.[3] Newton predicted refraction as a pull of the medium upon the light, implying an increased speed of light in the medium. However, Fizeau showed the speed of light in water to be less than in air, not more, by inserting a tube of water in the light path.[4]

References

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External links

  1. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

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  2. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  3. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  4. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
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