A man approaches a mirror at a speed of 1 ms-1 .how fast does his reflected image comes toward him?

Question

A man approaches a mirror at a speed of 1 ms-1 .how fast does his reflected image comes toward him?

Answer 1

Trick question, or at best very poorly-worded. The image isn't a physical thing and cannot "move towards him", it is just the result of light reflecting off the mirror. Relatively speaking the mirror is moving towards him at 1 m/s (using the man as the frame of reference), but to say the "image" is moving towards him too is rather bizarre - the mirror doesn't "contain" an image. The man and the "man in the mirror" would APPEAR to be approaching at 2 m/s, exactly as if two real people were walking towards one another both at 1 m/s, but I still think it's a bogus question.

Answer 2

The reflected image is located at the same distance behind the mirror as the man is in front.

So, the reflected image is moving at 1 m/s wrt the mirror.  

The relative speed is 2 m/s..

(note, just because something is not "real" does not mean it can't have a location, and a speed.  For instance, you can talk about the location, and speed of a shadow.  The location and speed of a virtual image can be discussed without this being a trick question at all!)

Answer 3

Sounds like a trick question.  The speed of light* is constant, no matter the frame of reference.

c = 3.0x10^8 m/s

*Yes, I realize that's in a vacuum, but in air the difference is negligible.

Now, at relativistic speeds (significant fractions of the speed of light), interesting things will happen to his reflection -- wavelengths of the light will doppler shift -- but it will still "come toward him" at the same speed of light.