Fizeau–Foucault apparatus

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

History

The gear method goes back to experiments of Galileo Galilei. Already in 1600 posted Galilei two people, each with a lamp ( with a flap to interrupt the light beam ) on two hills. The first is to open his lamp suddenly, the second is to do the same as soon as he sees the light of the first. The first then tries to estimate the delay between the opening of his lamp and the flash of the other. However, the speed of light is too high in comparison to the distance between the men, so as Galileo only obtained a value for the human reaction time, but not for the speed of light.

Fizeau replaced in 1849 in his attempt the second man through a glass ( this eliminates the distortion by the reaction time ) and the first man by a lamp with a rapidly rotating toothed wheel which blocks the light at regular intervals.

Experimental setup

Fizeau led his experiment along an approximately 8.6 km ( 8633 m) long route through near Paris. The light is from the light source (L ) to a semi-transparent mirror (S1) is passed, of the light through the rotating gear ( n teeth) to the second mirror (S2) is initiated from which it towards the observer (B ) ( again through the gear ) was reflected ( see chart). Now, the rotational speed ( f) of the toothed wheel was increased until the level of the second (S2) not met beam reflected on the return path to the gap, but on the following tines. The observer could no longer see the reflected light beam.

N has the gear teeth, then, the time to replace a tooth gap of the foregoing:

. ( The 2 because of a gear teeth gaps and there. )

Now, if the speed chosen so large that the reflected beam of light is no longer visible, the light that is just the time needed to the way to go twice. It follows from the value for the speed of light:

Fizeau are f = 12.6 revolutions per second and the number of gear teeth 720 and 700: In the French publication of 1849, the statement reads on 720 teeth ( " sept cent vingt dents " ), while the German edition of 1850 " seven hundred teeth " noted. <

The value obtained with this methodology, the Fizeau, ( 315 300 ± 500) km / s, so that was about 5 % higher than the correct value of around 299,792 km / s Reason for the inaccuracy were the short and the imprecision with which the speed of the gear could be determined. James Bradley had already in 1728 using the method of aberration, a deviation of only 1%. 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 and improved in the Fizeau method.

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