system
Given the following post, respond as if you're commenting on Reddit:
human
Does a horizontally moving mirror reflect any differently than an equivalently stationary one?

Scenario 1: You're in your bathroom looking at your mirror.

Scenario 2: You're standing perpendicular to some train tracks when a mirror strapped to a train passes by.

Given that the moving mirror is long enough so you can get a good look at yourself, are there any optical distortions? What if the train is moving relativistically?
gpt
Divide the mirror up into infinitely thin vertical slices, each moving at velocity *v* on a train headed to your right. Define *phi* as the angle at which you are looking at the train -- *phi*=0 is normal to the mirror; pi/2 looks at the front of the train in the distance. Also, let's say the mirror is mounted above the train, like a fin on a sailfish, and that you are on a platform so as to be up at the level of the mirror seeing it whiz by  -- I'll explain this addition later.

Each slice of mirror is moving away from you at *v'*=*v*\*arctan(*phi*). So naturally, there will be some Lorentz boosting when you consider light leaving your reference frame and interacting with the mirror. But, there should be an equal and opposite Lorentz boost on the way back, so no need to worry about rewriting the laws of specular reflection.

But there is the pesky detail of the light blue- & red-shifting when boosted into the new reference frame. If your mirror is transparent to X-rays, radio, or any other kind of EM radiation, then at some angles, the mirror will get a Lorentz boost sufficient to turn the mirror transparent to visible light in your reference frame. From your perspective, any visible light should pass right through the mirror at that angle. This is where having the mirror mounted on top gets interesting.

Strange bands would appear at certain angles of *phi*. (Noting the train's velocity and the location of these angles would be a kind of spectroscopy that would tell you about the material of your mirror.) At the center of these bands, the mirror should be transparent to visible light (or at least, as transparent as the mirror would be to X-rays, radiowaves, or whatever the light got boosted into). 

On the sides of each band would be a gradual transition between reflectivity and transparency, though. Looking at the transitions from left to right, you would see, on the left side, the mirror stops reflecting violet first. Instead, that color would be allowed *through* the mirror from behind, As you get closer to the center, the other colors would transition from reflection to transparency too. At the center of the band, it would be transparent. And at the right side of the band, the transition back to mirror would start with violet first, letting the red continue passing through until last.

Other commenters have pointed out that interaction time for light to bounce of a mirror is non-zero. This would make for an interesting distortion. You would see your reflection standing slightly to your right. You would not be looking eye to eye; your reflection would appear to be looking down the tracks a bit (just as you are). Without turning your neck, you could see more of the left side of your head (and less of the right) than usual. For sufficient *v*, you could look into your left ear canal by looking right!

Thanks for this really great question!