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If you move at $5$ $ms^-$$^1$ towards a plane mirror, your reflection moves $10$ $ms^-$$^1$ towards you.

But what happens if you're moving much faster, say $0.8c$?

Would your reflection move at $1.6c$, since it's not a physical object? Or is it still confined to the speed of light and you have to apply the Lorentz factor? Or, does some strange light-reflecting thing occur since you're moving so fast at a mirror?

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The mirror is equivalent physically to a legitimate person mimmicking you behind an open gap... so apply the same logic as two trains coming towards each other at relativistic speeds.

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