Fizeau. What is connection between fringe shifts and velocity?

lenfromkits

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.

DaleSpam

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.

lenfromkits

Thanks. I see, that makes sense. But that leads to a new question. Given the what we know about the Doppler shift, shouldn't the moving water have shifted the frequency as well?

DaleSpam

No. Why would it?

lenfromkits

It seems like it would - for the reason I mentioned. Doppler shift. Is there any documentation about this effect in this scenario?

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.

DaleSpam

What Doppler shift? The emitter is not moving relative to the detector.

Sure, in the case where the emitter is moving towards the detector. That is the usual Doppler effect and does not apply here since the emitter and detector are stationary wrt each other.

lenfromkits

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.

DaleSpam

No, it wouldn't, it would only change the speed and wavelength, not the frequency.

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.

lenfromkits

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?

DaleSpam

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.

lenfromkits

Thanks. Still trying to fully understand your comment "e frequency of the incident and the transmitted radiation must be equal or you will get a phase discontinuity at the boundary" in my own words.

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.

DaleSpam

You may want to rephrase that.

Sure, but the emitter and the detector are not moving towards each other in the Fizeau experiment. You really need to forget about the Doppler effect, it is completely irrelevant here.

No, the speed of light is always slower in air or water than in vacuum. It is never increased.

lenfromkits

I'm not sure what you mean by "it is never increased" The whole result of the Fizeau experiment shows that light speed increases. Speed of light when in a medium increases. My point is that speed of light in air also increases the frequency when the emitter moves, therefore implying that if the emitter moves in a medium then also the frequency would increase. You suggested I forget about the doppler effect but that's the whole point of my question. The question stems around one issue - does a moving medium have a similar effect on the frequency of light as a moving emitter? Clearly the answer is not clear. I appreciate your opinion, but what I need is actual experimental documentation to either refute or confirm that.

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.

DaleSpam

No, the speed of light in a medium never increases relative to the speed of light in vacuum. The speed of light is slowed down less if the medium is moving parallel to the direction of propagation than if it is moving anti-parallel, but it slows down either way.

No.

The Fizeau experiment does just that.

DrGreg

I think the two of you are talking at cross-purposes. Light in a moving medium can go faster than light in the same stationary medium (if the medium moves in the same direction) but always slower than light in vacuum.

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

DaleSpam

Yes, which is why I said:andI don't know how I could have been more clear.

DaleSpam

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.