The only reason people think mirrors have left/right reversal and not up/down reversal is because when they turn the object around to view it in the mirror, there is almost 100% tendency to turn the object around a vertical axis rather than a horizontal axis.
Do this. Take your physics book (or a magazine) and stand in front of a mirror. Hold the book so you are looking at the front cover directly, and you can read it. (In the mirror you see the back cover of the book.) Now, turn the book around so the front cover is away from you, and you now see the front cover in the mirror. If the wording looks left/right reversed in the mirror it's because when you turned the book around, you turned it around a vertical axis, which is what almost everyone does.
Now, return the book so the front cover is again facing you, and you can read it. Turn the book around again, so the front cover faces the mirror, but this time turn it around the appropriate horizontal axis. Now when you view the front cover in the mirror, the letters are upside down, but left to right correct.
In the first case, the mirror didn't reverse the right and left... you did... when you turned the book to face the mirror. In the second case, the mirror did not reverse top and bottom... you did... when you turned the book to face the mirror.
Get some self-adhesive letters, perhaps 1 or 2 inches tall, and stick them on a sheet of quarter-inch thick Plexiglas, Lucite, etc. You might trying putting the words...
TOP
LEFT RIGHT
BOTTOM
On the acrylic sheet.
Stand in front of the mirror and hold this sheet in front of you so you can read the sheet directly. Then look in the mirror without turning the sheet. Everything looks fine. TOP is on top, RIGHT is on the right side, etc. All the letters face the correct way both on the actual sheet and also the mirror image of the sheet.
But the letters on the sheet in the mirror are on the opposite side of the plastic sheet from where you are standing, whereas the letters on the real sheet are on the same side of the sheet as you are.
Even more instructive, drill a hole in the sheet so you can stick something like a sharpened pencil through the hole and glue it in place. In the actual acrylic sheet, point the pencil away from you. (The sharpened end is behind the sheet when you read the words, and the eraser end is toward you. Now look at that sheet in the mirror while you are holding the real sheet so you can read it. Although the words in the mirror are perfectly readable, the pencil in the mirror is pointing toward you whereas the pencil you are holding in your hands is pointing away from you.
If you are a half-ways decent gymnast, or can recruit one... stand yourself (or the gymnast) in front of the mirror but facing away from the mirror. Now turn yourself (or the gymnast) to face the mirror, but don't turn around the normal way. Instead, lean over backwards and go into a headstand. Look at yourself (or the gymnast) in the mirror. The image of the person in the mirror is upside down. Of course... you or the gymnast are/is also upside down. But that's the same principle as when you turn to face a mirror using the normal procedure. If you are facing way from the mirror and you turn around to face the mirror, you turned yourself (and your image). The mirror didn't turn you or your image.
Now get a mirror that you can hang or stand so you can access both the back and front. Stand on the side so you can place the palm of your right hand against the front of the mirror. Place your left palm on the back of the mirror right behind your right palm. Now slowly drag both hands either toward the top of the mirror or toward the side where you are standing. You and your students should watch your right hand and its mirror image as you do this. When your hands arrive at the edge of the mirror, keep going. As the right hand begins to "clear the mirror" we begin to lose its image, but your real left hand takes its place. Like magic we see that the image of your right hand that was in the mirror has suddenly manifested itself as your real left hand. (It's even better if you take off any rings or watches or bracelets.)
Oh... so the mirror does reverse left and right. Yes, but not left/right directions. Rather, it reverses left handedness and right handedness. It reverses the chirality of chiral objects. Your hands are chiral. They are mirror images of each other. But the pulling out of your left hand from behind the mirror until it joins palm-to-palm with your right hand shows that the chiral objects are "reversed front to back." The palms of your hands are facing opposite directions, and the backs of your hands are facing opposite directions. When your hands were on opposite sides of the mirror, one was in front of the mirror and one was in back of the mirror. The reversal is from the front side to the back side.
I think chemists might be a bit more aware of this than many physicists because chirality is a big thing in organic chemistry and biochemistry. We have our students sit at tables with chemical model kits and with mirrors attached to wooden bases to hold them vertical. They build a chiral molecule in front of the mirror, then they look into the mirror while building a second molecule that matches what they see in the mirror. When the second molecule is finished, they compare it to the first molecule and discover there is no way to turn it or orient it so it aligns perfectly with the original molecule. That's a chiral molecule.
BTW. I still use the word perverted. Who cares if some people use the word to describe people who have some unusual characteristics. If students get a kick out if it, then it just helps them remember it better. If you Google perverted + physics or perverted + mirror you will get lots of hits of physicists using the word for mirror images.
Michael D. Edmiston, PhD.
Professor of Chemistry and Physics
Chair, Division of Natural and Applied Sciences
Bluffton University
Bluffton, OH 45817
Office 419-358-3270
Cell 419-230-9657