The various feynman "fun to imagine" videos, one of which is linked by the answerer, are amazing. I advise you to watch all of them as soon as you can. They're all up on youtube as linked on stackexchange, or you can see them on the BBC's site here: http://www.bbc.co.uk/archive/feynman/
Also, feynman's explanation is much more intuitive and more easily understood than the one given on stackexchange. As you might imagine. Also it comes replete with the inevitable feynman tales of intellectual dickswinging that we have all come to know and love.
Feynman says some interesting stuff but none of these explanations have yet satisfied me. Sure, I get it that a mirror technically does not rotate the image, it does the near/far thing instead, flips the nose, flips the north/south, however you want to put it.
But, this the fact remains: I hold an object in front of me (there is no mirror anywhere). IF I want to see/simulate what the object will look like in a mirror, I rotate it LEFT TO RIGHT (on the vertical plane, around the line that is parallel to my body no matter whether I am standing or laying down). I cannot rotate it any other way and get the same effect. WHY is that?
EDIT: Whoops, you guys are all right, I'm an idiot. Here I am sitting at my desk with quite literally nothing but bisymmetric objects around me- for a second there I went a little crazy. Thanks for setting me straight
Rotating an object left-to-right most certainly won't show you what it looks like it a mirror. It shows you the back of the object (assuming that the front of the object was previously facing you).
Here's an experiment to demonstrate that left-to-right rotation is not what a mirror does.
1. Take an object and hold it so that the front is facing you (pick a side and call it the front if there's not an obvious "front").
2. Rotate the object left to right so that you are looking at the back.
3. Write your name on the back of the object (the side currently facing you).
4. Rotate the object right-to-left so that the front is once again facing you.
5. Go to a mirror and hold the object so the front is facing you.
6. Look at the object in the mirror.
Does the object in the mirror look the same as when you did the left-to-right rotation? No. You can see the back of the object, but your name is backwards. What you're seeing in the mirror is not a left-right rotation. That's an explanation that your brain applies to the situation, but it's not what actually happens.
A similar experiment is to hold a coffee mug and stand in front of a mirror. Grasp the mug by the handle with your right hand. Look in the mirror. Where is the handle? It's still on your right. The coffee mug in the real world has the handle on your right, and so does the coffee mug in the reflection. There is no left/right reversal.
Edit: You're not an idiot. The mirror's behavior is simple, but it's also very non-intuitive. If it were intuitive, people wouldn't ask the question.
It's psychological. You could instead rotate the object head-over-heels to "simulate" reflection, and the object would then appear upside-down, but have left and right in the same position as on a mirror. However things don't normally move head-over-heels but rather by rotating left/right (thanks to gravity) so psychologically, we assume the object must have rotated left/right to get on the other side of the mirror, thus appearing reversed in that direction.
I don't know about you, but if I turn a picture-postcard around its vertical axis, left-to-right, all I see is the blank back of the picture. (Likewise if I rotate it around it's horizontal axis.)
What you're actually saying is if I put the picture on transparent acetate (or whatever) and rotate it, then look at it through its back, I see the same as I would in the mirror. Which is essentially the same as reversing the depth of the object (when you think about it.)
And there's nothing privileged about the Left-to-right rotation. When you face the mirror and hold the picture up (facing the mirror, away from you), you chose to rotate it around its vertical axis to face the mirror (thus swapping left and right). If you chose to rotate it around its vertical axis, top-to-bottom, to face the mirror and away from you then you get the other situation.
It doesn't flip left to right. It flips front to back. Hold something in front of a mirror; you > thing > mirror > thing > you.
It reorients things 'on the vertical plane' parallel to your body because your eyes are perpendicular to your vertical orientation and your brain is used to processing things that way. Put a mirror on the floor or the ceiling and mess about with some geometric solids for a while, you'll start to think differently about it. Alternatively, get some dark safety goggles, a laser, and a bunch of small mirrors on adjustable fixtures.
The video says, "Not available in my area"! I don't think they realize I'm in the USA. The U-S-A! Everything is available to me. How could anyone let this happen?!
That's surprising: I thought YouTube's unit of granularity was the country. I'm in the US too and can see the video. I guess this means it's available in some parts of the country and not others. Hurray for being in Boston, then.
It's funny - that series of videos is exactly the sort of video that would make someone a YouTube star today.
In the same way a teenage girl gains a following after making videos of how to apply makeup, I could easily see Feynman becoming a similar YouTube phenomenon had he lived now and released videos like this on a regular basis.
Always fun to imagine people from another era who you know would have been MASSIVE on social media (another one: Robert Townsend -> Twitter).
Also, feynman's explanation is much more intuitive and more easily understood than the one given on stackexchange. As you might imagine. Also it comes replete with the inevitable feynman tales of intellectual dickswinging that we have all come to know and love.