A question that has been puzzling me for ages

The question (or a variation thereof) was on an Oxford Physics entrance paper, and said:

If you approach a mirror at 5ms^-1, at what speed does your image approach you?

I think the answer depends on how you define an image, but I think it's 10ms^-1, because the image is virtual and appears "behind" the mirror, approaching you at -5ms^-1.

How far has the light travelled that reaches your eye? Millions of km.....

But the image isnt moving, at least not towards you anyway. The image doesnt approach you, you approach the image. no?

The image is moving. You move toward it, and it toward you, as its position is dependent upon yours.

As you move towards the image, its virtual position changes, coming towards you at the same time. It can't stay in the same place no matter your position, otherwise you would see the same image in the mirror if you stood at a completely different distance or angle! As you move in at 5ms^-1, it moves out at 5ms^1, so you approach it at 5ms^-1 - - 5ms^-1 = 5+5 = 10 ms^-1.

the light is traveling 10m so i'd say that.

Virtually, yeh i agree the image moves. But not at 10ms^-1, that would mean the image is moving faster than you are!

The image moves at 5 in the negative direction

You move at 5 in the positive direction

So you approach eachother at 10

But in answer to the original oxford question, the virtual image is approaching at 5 yes?

No it isn't...

an on the how fast is it moving towards you question, wont it be the speed of light?

No that isn't what it means, in a frame where you are stationary (i.e. from your point of view) the image moves towards you at 10ms^-1. The light moves at the speed of light yes, but this light is how we see the image, not the image itself if you get what I mean.

It depends what you're looking at. If you're looking at the mirror, 5m. If you're looking at yourself in the mirror, 10m.