Optics - Reflection of image from a moving mirror

[Saw]

Good answer. Thanks for the reply.

Let's tweak the setup a bit then. The radio transmitter is now on the moving platform along with the wire mesh surface. Someone in motion with these should of course always observe the signal to pass through the surface, as when the platform is at rest. However, at a certain speed, an observer on the ground will see both a contracted mesh and a lengthened wave to the extent that the signal should reflect. Which actually happens?

Is this subject the same / analogous to the one treated here?

 

[chaimc]

(I, myself, am not a phisicist.)

1- Yuiop, on mesage #27 sent me to learn about time dilation. Apart from the interpataion of the famous Michelson Morley experiment, what other evidence is there to Time dilation?
2- Historicaly, where there any other interpretaions of that experiment?


3- I got lost somehwere along the line when "you people" started talking abput radio waves - is their behaviour identical to light waves?

 

[Austin0]

Good answer. Thanks for the reply.

Let's tweak the setup a bit then. The radio transmitter is now on the moving platform along with the wire mesh surface. Someone in motion with these should of course always observe the signal to pass through the surface, as when the platform is at rest. However, at a certain speed, an observer on the ground will see both a contracted mesh and a lengthened wave to the extent that the signal should reflect. Which actually happens?

Interesting question.
My thought is that, no matter the velocity, the signal will pass through the mesh and be detected by the ground observer but it will, in all cases, be blue shifted rather than red.
Due to the aberration from the relative velocity the signal path in the ground frame would not be orthogonal but would be at some forward angle and therefore blue shifted.

Or not ;-) In which case you have come up with a thorny one.

 

[Saw]

the signal will (...) be blue shifted rather than red.

I have a problem with any explanation resorting to blue or red shift: isn't it a position dependent question? When the moving source is approaching, the observer sees the signal as blue-shifted. Instead another observer in the same frame, for which the source is receding, sees the signal as redshifted. However, it seems the answer to the question "what happens" should be the same in all frames and from all positions of those frames...

 

[Austin0]

I have a problem with any explanation resorting to blue or red shift: isn't it a position dependent question? When the moving source is approaching, the observer sees the signal as blue-shifted. Instead another observer in the same frame, for which the source is receding, sees the signal as redshifted. However, it seems the answer to the question "what happens" should be the same in all frames and from all positions of those frames...

Hi Saw ,,,long time. In general you are quite correct regarding position dependence but in this setup there are limitations.
Assuming a flat mesh, aligned parallel to travel, then the only signals that would pass through in the train frame would be those traveling from the emitter on an orthogonal path [with some limited deviation] relative to the screen. Those outside this narrow angle would be reflected.Clearly this path, which is orthogonal in the train frame, is at some forward angle in the ground frame.
So if the observers were lined up along the track , only a limited number of observers, falling within this narrow sector at any given time, would receive the signal. But this is expected because the other observers ,further up and down the line would be at too acute an angle [wrt the mesh ] to receive a signal in any case.
It seems unlikely there could be a red shift. For this to occur the path angle would have to be toward the rear in the ground frame. Since aberration shifts emited path angles in the train frame, forward in the ground frame, for a signal to have an angle toward the rear in the ground frame would require the emitted signal to have an even greater angle toward the rear in the train F and also wrt the mesh.
Having thought it over it would also depend on boundary conditions. Distance of emitter from mesh, wavelength etc. I guess if the conditions were loose enough and a wide enough angle of signals could pass through the mesh then some red shifted signals would be observed on the ground.
In this case it seems like it would still only be observed by a limited number of observers at a time but then each would receive a changing signal, shifting from blue through the spectrum to red.
Interestin scenario. Thoughts?

 

[Saw]

Hmm. Yes, you are right in that, to determine what happens, what matters is how the signal arrives (red or blue shifted) in the position where it arrives. You are also right in holding that the signal is blue shifted in the sense that, in the ground frame, the signal is projected with a direction that has two components, one in the Y axis and another in the +X axis. Peak n, since it is emitted later than n-1, is emitted from a place that is farther away from the origin in the +X axis of the ground frame. However, the peculiarity here is that no single observer receives all peaks. If you make observers small enough, you would get one observer for each peak...

Is this what is called transverse Doppler shift? I read the wikipedia entry on Relativistic Doppler Shift and the section on the Transverse one, but did not understand what it says about the latter.

 

[Austin0]

Hmm. Yes, you are right in that, to determine what happens, what matters is how the signal arrives (red or blue shifted) in the position where it arrives. You are also right in holding that the signal is blue shifted in the sense that, in the ground frame, the signal is projected with a direction that has two components, one in the Y axis and another in the +X axis. Peak n, since it is emitted later than n-1, is emitted from a place that is farther away from the origin in the +X axis of the ground frame. However, the peculiarity here is that no single observer receives all peaks. If you make observers small enough, you would get one observer for each peak...

Is this what is called transverse Doppler shift? I read the wikipedia entry on Relativistic Doppler Shift and the section on the Transverse one, but did not understand what it says about the latter.

If by peaks you are referring to wave peaks then of course every observer gets a full set [i.e.at least one photon] otherwise you must explain what you mean.
On the two components. If a signal has a positive x component in direction it is blue shifted if negative , red shifted.[assuming +x travel]
I'm not sure but I think this is transverse Doppler in a nutshell. I believe the math is simply the R Doppler with the inclusion of the trig to calculate the variation with angle.But may be wrong
My assumption is that you have maximal blue shift on distant approach, maximal red shift on distant recession and then shift through the spectrum in between in passing, as the angle changes. At some point having no shift, probably at the closest point. If this is incorrect hopefully someone will supply the right picture.ciao