RPM of Fizeau-Foucault apparatus?

[rkbrooks]

Hi All,

 

First post here, please be kind.

 

I recently visited the Musée des Arts et Métiers during a trip to Paris- which btw, is very nice- a little short of explanations, but what a collection! In any case, they had, what I assume, is an original version of the Fizeau-Foucault apparatus.

 

The rotating mirror mechanism was pneumatic, and I was wondering what sort of RPM this thing could achieve? Now, I can calculate what type of displacement they'd get on a return beam based on distance and angular speed, but I only can find a reference to the distance (20 miles one-way).

 

TIA for any insight or references!

 

-Ryan

[cbq]

I haven't been able to confirm the actual rotation speed when the experiment was performed, but it is possible to get a rough idea using the applicable formula for estimating the speed of light, which is: c = da/dt x 2h/a, where h is the distance between the mirrors (the 20 miles you noted) and a is the angle the rotating mirror traverses while light travels this distance. The experimenter would measure an angle of deflection of the mirror that is twice a to come up with an estimate of the speed of light. Knowing the speed of light, the speed of mirror rotation can be calculated for various values of the deflection angle. The formula can be restated as da/dt = a x c/2h, or da/dt = a x 186,000 mi/sec / 40mi, or da/dt = 4650 x a degrees/sec. If the experimenter measured an angle of deflection of 4 degrees, then a=2, and da/dt = 9300 degrees/sec, or approximately 26 revolutions per second!

 

See: http://en.wikipedia.org/wiki/Fizeau%E2%80%93Foucault_apparatus

[Enthalpy]

If they observed a deflection of 60m over 35km between the rotating mirror and the observers, then 0.1° was enough, needing only 1.7s per turn. Impressive sensitivity.

[swansont]

If they observed a deflection of 60m over 35km between the rotating mirror and the observers, then 0.1° was enough, needing only 1.7s per turn. Impressive sensitivity.

 

The 35 km is not between the rotating mirror an observer. That's the distance between the moving and fixed mirrors. The distance to the moving mirror is not needed if you solve for the deflection angle.

[Enthalpy]

I expect them to have observed a deflection distance to know the angle, and a long path allows to measure angles more precisely.

Then, two options:

- Observe the spot at the same experiment site as the rotating mirror. Less sensitive, but limits people's travels. Probably what they did.

- Have the rotating mirror at one site, the fixed one and the observed spot at the other. More sensitive, but complicates the interactions between the crews at the rotating mirror and the observed spot. The one I had imagined.

 

As they chose 35km, it was probably the first option, yes. The second would have allowed a distance like 1km.

[Enthalpy]

Fun: the historical experiment could easily be reproduced at a school, university...

 

Taking all legs 100m long this time, and rotating the mirror at 100Hz (6000 rpm) with a small DC motor, the deviation is 42mm, wow. A laser pointer diverges too much over 300m, but with an additional lens? Or maybe a halogen lamp, a lens and a far enough collimator?

 

The rotatig mirror should better have many polished facets to increase the received light intensity.

Edited June 20, 2013 by Enthalpy

[swansont]

Fun: the historical experiment could easily be reproduced at a school, university...

 

Taking all legs 100m long this time, and rotating the mirror at 100Hz (6000 rpm) with a small DC motor, the deviation is 42mm, wow. A laser pointer diverges too much over 300m, but with an additional lens? Or maybe a halogen lamp, a lens and a far enough collimator?

 

The rotatig mirror should better have many polished facets to increase the received light intensity.

We did this in a lab in college 30+ years ago, using a HeNe.

 

The divergence doesn't matter; you put the collimating slit just after the light starts on the first leg, which narrows the return beam before it hits the mirror. The advantage here is that the laser is pretty bright, so you can use a narrow slit and measure a small deflection angle pretty easily.

[John Cuthber]

 

We did this in a lab in college 30+ years ago, using a HeNe.

But it's more fun to use a microwave and a tray full of marshmallows.

[swansont]

But it's more fun to use a microwave and a tray full of marshmallows.

 

I prefer chocolate, but yes, it's a good way as well. Except that you have to trust the manufacturer gave you the right frequency. With the rotating mirror, you can measure all the variables.

[John Cuthber]

I think it's worse than that. I'm fairly sure that the wavelength of the µwaves is related to the spacing of the electrodes in the magnetron cavity.

So, what you are actually doing in that experiment is indirectly measuring the size of a bit of metal by measuring the space between blobs of melted chocolate..

However, if you have a really good frequency counter and can verify the µwave frequency it's a valid measure of c and, if you don't, it's still an excuse to buy lots of swets.

[Enthalpy]

 

We did this in a lab in college 30+ years ago, using a HeNe.

Nice college! I'd have preferred that to experiments with falling balls... And sure, a good source makes it easier.

 

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RKBrooks, if you liked the Musée des Arts et Métiers, you should try the Deutsches Museum in Munich. Much bigger, better explained, with nice historic pieces as well (Siemens' electric railway engine, first induced fission, things from Lilienthal and Wright...) and more actual technology.

 

And the Technorama as well, in Winterthur.