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Last week I came across with a question from an old course I took in General Relativity which said this:

Suppose you are traveling at speed v=0.9c respect to an observer who remains standing up still aside and you are carrying with yourself a mirror in front of you.

How would you see your image reflected from the mirror?

The teacher told us the image would seem the same for us as if we were not moving at all, since we are moving with the mirror itself at the same speed and light comes at speed c onto its surface and reflects at the same speed and thus, there is no alteration.

Now, I asked myself a "small" variation to the problem. What about the observer remaining still who sees me moving at that speed?:

  1. I assume that the image would look a bit distortioned towards a direction, considering that there is length contraction appearance always towards the direction of movement. But that does not affect light's reflection and arrival, since it will be seen at the same speed c. I am only talking about the picture of me in the mirror itself being seen by the other guy. Am I right?
  2. If the distortion I speak about above does not exist (at least due to length contraction), is there an aberration or focus effect present due to the angle in which the observer would watch my image? I remember having studied or read about some of these too years before.
  3. I guess my image would seem shifted to the red spectral region, due to a Doppler effect caused by my speed.

This questions naturally ran into my mind when thinking about the problem. I can think of the 3 of them taking place, but I can't help feeling confused when asking myself whether all of them can take place or not. Under which conditions could I have them all?

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Length contraction of the image or i can say "the whole mirror"will dedends on the orientation of mirror in your hand and the direction in which you are running with respect to observer.For example if you are moving in any particular direction and the area vector of mirror surface is parallel or antiparallel to the direction of motion with respect to the observer then there will be no length contraction in the image, provided your image can be seen by observer.Now if you held the mirror in such a way that area vector of surface of mirror is perpendicular to the direction of motion with respect to observer then their will be maximum contraction of length.Yes red shift will occur if you are moving away from him and blue shift will occur if you are moving towards him

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