Gear method

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Fizeau's historical experimental setup based on François Arago

The gear method is a method of determining the speed of light , which was developed by the French scientist Hippolyte Fizeau in 1849 .

history

The cogwheel method goes back to experiments by Galileo Galilei . As early as 1600 Galileo posted two people with a lamp each (with a flap to interrupt the light beam) on two hills. The first should suddenly open his lamp, the second should do the same as soon as he sees the light of the first. The first then tries to estimate the delay between opening his lamp and the flashing of the other. However, the speed of light was too high compared to the distance between the men, which is why Galileo only received a value for the human reaction time , but not for the speed of light.

In his attempt in 1849, Fizeau replaced the second man with a mirror (this eliminates the falsification of the reaction time) and the first man with a lamp with a rapidly rotating gear that blocks the light at regular intervals.

Experimental setup

Experimental setup for the gear method

Fizeau conducted his experiment along a stretch of approximately 8.6 km (8633 m) near Paris . The light was passed on from the light source (L) to a semi-transparent mirror (S1), which guided the light through the rotating gear ( n teeth) in the form of flashes of light to the second mirror (S2), from where it was directed to the observer (B) (again by the gear) was reflected (see graphic). Now the speed ( f ) of the gear wheel was increased until the beam reflected by the second mirror (S2) no longer hit the gap on the way back, but hit the next point. The observer could then no longer see the reflected light beam.

If the gearwheel has n teeth, then the time until one tooth takes the place of the previous gap is:

. (The 2 because a gear is made up of gaps and teeth.)

If the speed is selected so high that the reflected light beam is no longer visible, the light needs just the time to cover the path twice. From this follows the value for the speed of light:

Fizeau specifies f = 12.6 revolutions per second and the number of gear teeth as 720 or 700: In the French publication of 1849 the specification is 720 teeth ("sept cent vingt dents"), while the German edition of 1850 " seven hundred teeth ”.

The value that Fizeau achieved using this method was (315,300 ± 500) km / s, which was about 5% above the correct value of around 299,792 km / s. The reason for the inaccuracy was the short distance and the inaccuracy with which the speed of the gear could be determined. James Bradley had already achieved a deviation of only 1% using the aberration method in 1728 . A much more accurate determination of the speed of light succeeded a year later, in 1850 , with the rotating mirror method of Léon Foucault was modified in the Fizeau method and improved.

literature

  • Hippolyte Fizeau: Sur une expérience relative à la vitesse de propagation de la lumière. In: Compte rendu de l'Académie des Sciences, Volume 29 (1849), pp. 90–92 and p. 132 ( PDF on gallica.bnf.fr )
  • Hippolyte Fizeau: Sur une expérience relative à la vitesse de propagation de la lumière. In: Revue scientifique et industrial, Volume 36 (1849), pp. 393–397 ( full text in the Google book search)
  • François Arago : Mesure de la vitesse de la lumière par des observations faites sur la terre a de courtes distances . In: Astronomie Populaire , Volume 4, 1857, Issue 28, Chapter 13, pp. 418-425. ( on wikisource , PDF on gallica.bnf.fr )
  • Wolfgang Demtröder : Electricity and Optics (Experimental Physics; Vol. 2). 5th edition Springer, Berlin 2009, ISBN 978-3-540-68210-3 .
  • Roger Erb: The Fizeau experiment in a new guise . In: Physics in our time , vol. 36 (2005), issue 6, pp. 274-277, ISSN  0031-9252 .

Individual evidence

  1. Arago: Astronomie populaire , fig. 339 in volume 4, 1857, inserted between p. 416 and 417 in chapter 11
  2. ^ Fizeau: Sur une expérience relative à la vitesse de propagation de la lumière. 1849, p. 92
  3. Fizeau: Attempt to determine the speed of light propagation . In: Annalen der Physik , Volume 155 (1850), pp. 167–169, ( online at the French National Library )