Optics - Reflection of image from a moving mirror

[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