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Why mirrors work isn't such a hard question. That's a matter of optics and how light reflects. I've never seen a good answer to the first question--and I've seen answers from mathematicians, physicists, and philosophers. But, I guess I'm not even sure what a good answer would look like. So far, none of the answers I've come across seem compelling to me.
I think the best way to think of it is because your focus isn't changing, but your point of view is.
When you look at a mirror your focus is placed on the mirror. That focus is then reflected back at you and so you are essensially seeing when you would see if you were standing where the mirror is, except you are seeing it where you are standing. Its a POV shift just as much as if you pointed a mirror at another mirror and tried to find the end of the reflection.
If you were to consider a mirror's reflection a transperant two dimensional picture you could turn around, then by flipping the reflection around you would get the original picture.
An up/down flip would be made when the object is beyond the point of focus. You can get it when you look through any lense that causes magnification because it is causing your focus to shift to a point closer than what you look at. When you hold it too close what you look at is out of focus because the point of focus is beyond the object. When you hold it just right the point of focus is on the object causing it to appear larger because you are taking a point of view much closer to the object (the lens is acting as your eye). When placed too far away from the lens the focus is going beyond the point so that the top of your view is on the bottom and the bottom of your view is on the top resulting in an up-side-down view.
The Upside Down view is easily achieved through magnification lenses because it forces the focus on a static point. In theory we could see the world that way if we focused the lens of our eye to a point too close to what we want to view, but our brain and automatic responses prevent that.
Then again...that's just my understanding of the theory. Its somewhat similar to how you can make your eyes go out of sync and create visual illusions or the theory behind 3D movies and holographics.
My sanity is not in question...
It was a confirmed casualty some time ago.
Light, grant me the serenity to accept the things I cannot change, the courage to change the things I can, and the wisdom to hide the bodies of the people I had to kill because they ticked me off.
You want complicated? Supposedly relativity says that all frames of reference are equal. Explain how standing in a rotating frame (eg. a centrifuge) makes you equal to those in a stationary frame. Does the math say that the view that the universe is rotating around the guy in the centrifuge is just as valid a POV as that the universe is stationary and the centrifuge is rotating?
Dude, seriously, WHAT handkerchief?
snooggums' density principal: "The more dense a population, the more dense a population."
Iliana: "You're a great friend but if we're ever chased by zombies I'm tripping you."
If you turn your head sideways, the mirror will reverse top/bottom instead of side-to-side! :p
I think the mathematical answer is that a side-to-side reflection is actually equivalent to a top-to-bottom reflection, with the sole difference of the reference direction chosen as "down" in the final image. That direction is chosen by your mind when you look at the image, but tends to correspond with the "down" experienced by your inner ear, and it is that correlation that forces the image to appear to have undergone a horizontal reflection instead of a vertical one.
Ever hit tennis balls off a wall? If you think of photons as tennis balls, and think of a mirror as a special wall that reflects photons, I think it becomes clear that any "reversing" that happens is in your brain, not in the mirror. All the mirror does is make photons bounce off of it.