Velocity of Image approaching mirror

[rktpro]

I came across this while reading--If an object approaches/moves away from a mirror with velocity v then the image approaches/moves away from the mirror with velocity 2v. Isn't this wrong? The image should approach/move away from object with 2v rather than from mirror.

Thanks.

[Marqq]

I came across this while reading--If an object approaches/moves away from a mirror with velocity v then the image approaches/moves away from the mirror with velocity 2v. Isn't this wrong? The image should approach/move away from object with 2v rather than from mirror.

Thanks.

 

Before some special relativity guys ruin this simple question: YES! You are correct. Classically speaking, your understanding that the speed of the object's reflected image relative to the object could be approximated as 2v (with less accuracy as the object's speed approaches c) is perfectly sound. Though I already qualified the hell out of that last sentence, I should also include that this only counts for movements directly toward or away from the reflection, lateral movement, obviously, would not stack.

[rktpro]

Before some special relativity guys ruin this simple question: YES! You are correct. Classically speaking, your understanding that the speed of the object's reflected image relative to the object could be approximated as 2v (with less accuracy as the object's speed approaches c) is perfectly sound. Though I already qualified the hell out of that last sentence, I should also include that this only counts for movements directly toward or away from the reflection, lateral movement, obviously, would not stack.

 

Book of such good author and still mistakes. Thanks buddy.

[Schrödinger's hat]

Before some special relativity guys ruin this simple question: YES! You are correct.

 

Aww, but please.

Why you gotta spoil the fun?

[rktpro]

Aww, but please.

Why you gotta spoil the fun?

 

You must be the relativity guy.

Let's see what you people say about it.

[Schrödinger's hat]

Well, first we'd need to decide on whether we'd be talking about the light you'd see, or the light you'd measure.

 

Let's go with see. In the frame of the guy the image is of.

 

There's a few different effects to take into account:

1. The mirror encounters light with less and less time delay as it approaches, giving the impression of speeding up the man in its reflection.

2. The light leaving the mirror is doppler shifted, giving the appearance of speeding up the image you see in it.

3. Aberration comes into the mix somewhere as well, these two effects somewhat take care of it (treating it as light delay rather than aberration), but I'd have to check to make sure the angular effects are included.

 

In all these would add up to the image in the mirror looking like it's moving at quite a clip. Anywhere between 2v (for low speeds) and infinity (as the mirror approaches the speed of light).

 

I'd have to do some reading or spend a while calculating to tell you exactly how fast, but double the apparent (aberrated) speed seems like a good guess.

[rktpro]

I am getting interested in relativity. I would read some when I get time!