How does light reflect off a moving angled mirror?

[h1a8]

Let c be the speed of light. I have a mirror in the north facing me but angled at 45 degrees north of east. I shoot a beam of light north towards it. But right before I send the beam the mirror has a velocity v towards the east. When the beam strikes the mirror does it reflect off at a right angle from the direction the beam was first shot (like it does when the mirror is not moving) or does it reflect off the mirror a different angle [like 90-arctan(c/v) degrees south of east]?

 

[K^2]

Both the angle and frequency will change, but I'm not feeling up to deriving the actual formula right now. Basically, the electric field in the outgoing wave must perfectly cancel the electric field in the incoming wave. If you consider a polarized, monochromatic, coherent plane wave, you should be able to derive the outgoing angle.

 

[h1a8]

Both the angle and frequency will change, but I'm not feeling up to deriving the actual formula right now. Basically, the electric field in the outgoing wave must perfectly cancel the electric field in the incoming wave. If you consider a polarized, monochromatic, coherent plane wave, you should be able to derive the outgoing angle.

Thanks! I was thinking more towards the topics of relative velocity and angle of incidence = angle of reflection. For example, if a beam moves north while a mirror, who begins perpendicular to the source (or facing it), moves east at velocity v then the velocity of the beam relative to the mirror would be (-v,c) making the angle of incidence arctan(c/|v|).
But if the mirror starting off tilted at 45 degrees north of east then the angle of incidence would be pi/4+arctan(c/|v|).

 

[K^2]

There are some fundamental problems with treating light as an "object" traveling at c. Sometimes it works out. Others, it gives you an error by some fixed factor, like the light beam being bent by gravity, the angle will be exactly 2 times off. Sometimes you get the exact opposite effect, like in refraction, where the light would bend the other way if it behaved like a particle.

There are also concerns with relativity. How does you approach account for relativistic Doppler shift when v->c?

Usually the best approach is to byte the bullet and work out what will happen to an electromagnetic wave.