What do Mirrors Really Do?

Many people think that mirror images are images that are flipped top to bottom or left to right, but that is not the case. Dianna Cowern (Physics Girl) explains what mirrors do in the following video.
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So mirrors don’t flip length, vertical, or top to bottom (what Physics Girl calls “Y axis"), and mirrors don’t flip horizontal, width, or left to right (what Physics Girl calls “X axis”). Mirrors seemingly do the equivalent of flipping depth, or front to back (what Physics Girl calls “Z axis").
 
To understand this better look at a 3 second scene from the film Terminator-2: Judgement Day in the video below. The scene takes place at minute 1:12 when the old terminator model, T-800 (played by actor Arnold Schwarzenegger) slams the new terminator model T-1000 (played by actor Robert Patrick) against a wall.
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​In this scene, the T-1000 terminator (which is made up of a “mimetic metal polyalloy”) flips itself front to back. His left hand becomes his right hand and vice versa, but his left hand is not flipped horizontally in the opposite direction to occupy the position previously occupied by his right hand. Mirrors do the equivalent of the effect portrayed in this scene. As Physics Girl explained in the video, when things appear to be flipped top to bottom or left to right by a mirror, it is us who are doing the flipping either by manipulating objects or by positioning ourselves or the mirror in the wrong direction. An example of this can be seen in the video below.
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​This video was shot at the Rosenberg Palace (former Institute for noblewomen) in the Prague Castle complex in the city of Prague, Czech Republic. The room contains the Baroque Holy Trinity Chapel and the Chapel of the Immaculate Conception of the Virgin Mary.

​It seems that to ease the strain on the necks of visitors contemplating the superb art on the very tall ceiling, a mirror was installed on the floor. Alas, the mirror was installed at an angle facing the visitors that come through the door. As a result of this frame of reference, the image in the mirror appears flipped vertically with respect to the image on the ceiling. Some people looking at this would conclude that mirrors flip images vertically, but that is not the case. The correct positioning of the mirror should have been slanted in the direction of the man in the video standing behind the mirror. This would have maintained the image’s true orientation.