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Fizeau. What is connection between fringe shifts and velocity? 
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#1
Mar2311, 02:58 PM

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When Fizeau (and Michelson and Morley) measured the fringe shifts that occur when light travels through a moving medium, how exactly (in words) did they deduce the change in velocity? My understand is this:
1) Count the fringe shifts that occur. 2) Calculate what the frequency shift must have been based on those fringe shifts. 3) Calculate what the velocity shift must have been based on the frequency shift. So, my real concern is with #3. What is the relationship that they used between the frequency and the velocity? Does a 1% increase in frequency translate into a 1% increase in velocity? This is puzzling because "normally" in a vacuum, a frequency change does not mean there is a velocity change (c is constant), so how do they manage to figure out what velocity change would be associated with a frequency change? Thanks for your help. 


#2
Mar2311, 04:16 PM

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It is not a frequency shift, it is a phase shift. The frequency is determined by the light source and is the same for both paths. The phase shift gives you the time delay, and the time delay combined with the path length gives you a difference in speed.



#3
Mar2311, 04:20 PM

P: 108




#4
Mar2311, 04:25 PM

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Fizeau. What is connection between fringe shifts and velocity?



#5
Mar2311, 04:37 PM

P: 108

Normally (in vacuum), adding to the forward motion of light decreases its wavelength and increases its frequency (no change in speed). This could be in essence described as "instead of the forward motion being added to the speed of light, the entire forward amount is translated into a reduction of wavelength and increase in frequency). In the medium, however, the forward motion 'does' add onto the speed of light  BUT only partially. "Part" of the forward motion results in an increase of light. The rest of the forward amount must then be attributed to a reduction in wavelength and increase in frequency. 


#6
Mar2311, 04:39 PM

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#7
Mar2311, 04:42 PM

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If a distant planet is moving towards us, then there is a blue shift. If the distant planet is stationary relative to us, then there would be no shift.
If light from a stationary planet is somehow 'boosted' along the way (like in the case of Fizeau) then it would have the same effect as the planet moving towards us, even though it is not. 


#8
Mar2311, 04:48 PM

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When you are doing EM problems and you have some boundary with incident and transmitted radiation the frequency of the incident and the transmitted radiation must be equal or you will get a phase discontinuity at the boundary. This is not particular to light, but is a feature of all kinds of waves. 


#9
Mar2311, 04:52 PM

P: 108

So in plain english, do you mean that: if the frequency in the Fizeau experiment 'HAD' been altered, then the resulting fringe pattern on the screen would have been a mess? Ie, the fringe patterns only show a fringe pattern if the frequencies are the same? Is that right?



#10
Mar2311, 04:56 PM

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No, in plain English, if the frequency in the Fizeau experiment had been altered then light would not be a wave and would not follow Maxwell's equations. You wouldn't be able to do interferometry at all if it weren't a wave.



#11
Mar2311, 05:07 PM

P: 108

The point you just made about waves and Maxwell, however, are not relevant for light  because the forward motion of a body on light DOES increase its frequency  aka Doppler Shift. The Fizeau experiment is kind of a hybrid between normal wave dynamics and light wave dynamics. The refractive index is a "continuum" such that for Fizeau and his water, the index was 1.33. For air it is 1.0003. Given that there is not clear difference between water and air other than they sit at different points on this refractive scale, when light travels through moving air  at least to some degree the speed must increase of the light (given that it is not an exact 1 refractive index). However  when light is boosted when travelling through air, we definitively see a frequency shift, implying that light through water would do the same thing, although just to a smaller amount. The only difference between the two scenarios is that in one case the light is 'boosted' by the emitter whereas in the other case it is 'boosted' along the way by the medium  which really narrows down the whole question to just this point  will that medium shift the frequency in the same way. I realize that I need to investigate this based on documentation about the experiment but have a hard time finding it which is really my question  where to find it. I have read several articles on the topic of the doppler shift in Fizeau's case, but they were arguments for Ether and blended in too much theoretical discussion for me to figure out what exactly is observed. 


#12
Mar2311, 06:07 PM

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#13
Mar2311, 06:45 PM

P: 108

So, can anyone in the forum provide any reference material to show if light traveling through a moving medium is affected at all in the same way as light being emitted from a moving body? Thanks. 


#14
Mar2311, 07:43 PM

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#15
Mar2311, 09:21 PM

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(All motion measured relative to the same observer, of course.) 


#16
Mar2311, 10:17 PM

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#17
Mar2311, 10:31 PM

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When the two paths of an interferometer have different frequencies the resulting interference is a beat pattern in time. This is called heterodyne interferometry. The Fizeau experiment was a homodyne experiment and had a spatial interference pattern, not a beat frequency. If the frequencies had shifted at all it would have been obvious as a flashing of the interference fringes at the beat frequency.



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