Re: A modification of Fizeau's toothed-wheel experiment

From: Eric Gisse (fsegg_at_!SPAMuaf.edu)
Date: 08/30/04 

Date: Sun, 29 Aug 2004 16:41:53 -0800

On Sun, 29 Aug 2004 20:01:24 GMT, The Ghost In The Machine
<ewill@aurigae.athghost7038suus.net> wrote:

[snip]

>>
>> The mirror is a fast-rotating [~1400 rpm, but lab notes are gone so I
>> am not sure.] 1 cm disc that is rotating about an axis so that the
>> mirror is on the circular flat side.
>
>Is this a crystal or merely a coating? Not that it would make
>too much difference, methinks.

Yes, No, Mabey so.

I don't remember.

>
>>
>> Laser. :p
>>
>> Reflector mirror, ~10cm in diameter.
>>
>> Half-mirror/microscope setup. I hope you have seen one of these
>> before.
>
>I can't say I've seen one personally, but the concept is
>not that unfamiliar to me; Michelson-Morley in particular
>depended on it.

If you really want to know, I can get the lab book for this
experiment. It includes part numbers :)

It is basically an adjustable microscope sitting above a half-mirror
to observe fringe shifts. It is a holy pain to adjust and read
properly. Im still not sure if I did it right.

>
>(I might even have one, although I have no idea now where
>I picked it up or where it's gone to. Basically, it was
>a small mirror less than 1 cm in radius, with a peculiar
>coating. It's probably gone now, and since I don't have
>a laser I've not tested it. Nor would I be able to use
>it properly even with a laser; the closest thing to a lab
>bench I have here is a couple of interesting desks from
>Sweden, which I bought because of their simplicity and
>because they supported my computers. :-) ) But they're
>on casters and hardly suited for anything even remotely
>approaching serious optical laser work.)

Not even close....this setup was to say the least, 'touchy'.

It might possibly work if you could stuff the whole apparatus onto the
1 table, but the path lengths needed kinda preclude that.

>
>> This is a standard half-mirror pushed into the beam path so
>> that some of the beam goes up to a microscope and some of it goes
>> forward. 2 polarizers are ahead of it taking down the intensity so you
>> don't *** up your eye.
>>
>> Between start and experiment is about 2 hours of aligning the fucking
>> thing. Oh boy. When someone says "step away from the mirror", they
>> MEAN IT :p .
>>
>> Laser ---> polarizers ---> half mirror ---> rotating mirror ---> flat
>> mirror ---> rotating mirror again ---> half mirror ---> microscope.
>
>Interesting setup. Not quite the same as my suggestion, but
>if reflection is a photon interacting with the atoms of the
>mirror, this should show something.

You are ahead of me as far as the mechanics of optics are concerned.

>
>>
>> More or less.
>>
>> What you observe with the microscope is the fringe shifting. God what
>> a pain in the ass.
>>
>> In case you haven't figured it out, the experiment on a whole is a
>> pain in the ass to do. Interesting, but painful.
>
>I'd say it's a pain in the back. :-) But it depends on whether
>one's standing or sitting -- it does sound tedious either way.

Sure as hell can't sit while doing it.

>
>>
>> Im still confused how I managed to observe c to be c/4. I was a factor
>> of 4 off to a few decimal places. Didn't *** up a derivation, ran the
>> numbers many times...*shrug*
>
>I'm wondering if it's a phase thing. Then again, I don't have
>your lab notes either. :-)

I don't have access to my lab notes. They are on a university server,
of which I am locked out from for a reason. :D

Getting my files is on the to-do list.

I think it is either a helluva co-incidence, because it was 4 to 2
decimal places out. Or i slipped a "4" somewhere in the derivation. If
I did, I missed it 3 times. Wouldn't be the first time I did something
like that but still :/

>
>>
>>>
>>>(IIRC, Fizeau directed the beam through the disk, then through a
>>>delay path, then through the disk again.)
>>
>> Sounds about right.
>>
>> As I remember, he adjusted the wheel's speed until he couldn't see the
>> light anymore, then he cranked the mathematical wheel and got a number
>> for c.
>
>That's also how I remember it. Interesting for its time;
>long passed history for us.
>
>>
>>>
>>>I'm not entirely sure what the best setup would be, but my
>>>computations suggest that this experiment:
>>>
>>>[1] is inherently doable, using something along the lines of
>>> current hard drive motors which can spin a disk at
>>> 10,000 RPM or more, leading to an edge velocity of
>>> about 157 m/s on a disc of radius 7.5 cm.
>>
>> Things that rotate that fast, that are not within an armored box,
>> scare me. Im the type of person who breaks things easily. I am sure
>> they exist though...
>
>Routinely. The more expensive disk drives spin at that speed.
>(Most consumer-level units might spin at 5400 or 7200. Check
>your manufacturer's specs for details.) The platter size
>has to be contained within the 3 1/2" form factor, which
>translates into a 8.89 cm width -- which makes such platters
>a bit smaller than your unit.
>
>Of course the platter isn't exactly toothed as I've specified,
>though it does have a very shiny surface. :-)
>
>I suspect you're misremembering it and that the actual
>speed was more like 14,000 RPM -- but of course I'm merely
>guessing here. My theoretical "envelope-back" calculations
>(I'll have to reprise them, but I posted them in another
>thread somewhere) suggest a wave-shift of maybe 1 lambda =
>500 nm at 10,000 RPM and a 1m optical path, were c' = c+v.
>But it's a less sophisticated measurement apparently than
>what you were doing.

No. It was 1400-ish, not 14,000.

We were not measuring doppler shifts, but instead we looked at
interference effects.

[snippage]