In the rear view mirror of your vehicle, the driver in the car behind is on the driver's side and the passenger is on the passenger's side. When they raise their left arms they are on the same side as your left arm. Why are the only things reversed the numbers and letters on license plate and the name of the car?
Contrary to piles and piles of common and well-intentioned explanations, a mirror doesn't reverse left and right. A mirror reverses towards and away.
If you are in your car facing to the north, and the driver behind you sticks out his left arm on the west side of his car, what you see in the mirror is a driver facing to the south with an arm stuck out on the west side.
We ordinarily describe this as a reversal of left and right because we use a cross product to define our relative directions. There are two choices for the direction of a cross product, distinguished by whether you use a "right-hand rule" or a "left-hand rule." But reflection in a mirror turns a right hand into a left hand, so images in mirrors disagree with us about the mapping of (up, forward, left) onto (up, north, east-west).
This question is related to a question often asked to trouble physics freshmen at the university. "Why, when looking in the mirror, right and left are reversed, although top and bottom are not ?".
Of course the question is asked so that it's more perturbing, and leads one to think in the wrong way about this issue.
A mirror reflects everything that is in front of it, so top remains top, bottom stays on the bottom, and... left on the left. Wave your left arm, and put yourself in the skin of your reflection, you'll feel that it waves its right arm. But you'll also feel that the tip of your head is at the tip of your head.
Hence left and right feel reversed because you have only one face, and you have to face the mirror with it, and you can't prevent from projecting yourself into the body of your reflection in the mirror.
This reversed letter thing is precisely the same, imagine you wear a t-shirt with text on it, that says "Hello". The "o" is on the left part of the shirt when you wear it. It will stay on the left part of the reflection. So your reflected self now wears a t-shirt with the "o" on the right side of it. Your reflected self wears a t-shirt that says "olleH". Note that he also dares using your left arm as a right arm, so he's definitely not to be trusted.
About the rear mirror, it just involves another person, but follows the same argument. It's like looking at someone looking at himself in the mirror. License plates are the t-shirt.
Just think about it a little in terms of light rays and reflecting surfaces (mirrors). The light rays from the right hand of the driver behind you are reflected by the mirror to reach your eyes on the right of the light rays from his left hand, so you see them that way. Likewise for his head and torso. But if you look straight at him, his right hand appears on the left and his left hand on the right. The letters are reversed for the same reason.
protected by Qmechanic♦ Feb 9 '14 at 15:28
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