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?
[Physics] Reflections in Rearview Mirror
geometric-opticsreflectionvisible-light
Related Solutions
Yes, it is possible.
Consider a mirror in the shape of a closed hemisphere - that is, half of a concave spherical mirror combined with a flat circular mirror passing through its center.
If you are inside this hemispherical mirror, you will see a real image of yourself rotated 180 degrees around the axis of the hemisphere. Here's one way to show this is true: The flat mirror creates a virtual image of you which is your reflection in the plane (duh), and the spherical mirror takes that as an object and creates a real image which is the inversion of that through the center of the sphere. The composition of the reflection and the inversion is a rotation.
Now, for practical reasons you don't want to be entirely enclosed by the mirror (it would be hard to get in and out, and you'd have to have your own light source...), so you could build just a part of the hemisphere. But the part you built would have to contain both some of the spherical surface and some of the flat surface for it to work.
If you have trouble understanding the orientation of everything, here is a concrete description: The flat mirror is a circle in the $z=0$ (horizontal) plane, $x^2+y^2\le1$. The spherical mirror is a hemisphere described by $z>0$, $x^2+y^2+z^2=1$. You're standing inside so your hand is at a point near the axis, for example, (0.01, 0, 0.2). What the mirrors do is this: For an object at a point $(x,y,z)$, the flat mirror creates an image at $(x,y,-z)$ (this image has opposite handedness because one coordinate is flipped). Then the spherical mirror takes that image at $(x,y,-z)$ and creates another image at $(-x,-y,z)$. This image has the same handedness as the original object. It is also "right side up" because the z coordinate is not flipped. The image of your right hand at (0.01, 0, 0.2) will appear as another right hand at (-0.01, 0, 0.2) which is in the appropriate orientation for you to shake hands.
The mirror is made convex in order to provide a wider field of view. Thus, the objects in it appear smaller than on a flat mirror, and your brain infers they should be further away.
Best Answer
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).