Mirror, Mirror, On the Wall

Men: If you're like me, you know that while you're waiting for your wife to pick out some clothes at a department store, when nobody is looking, you can't resist a surreptitious examination of yourself in those mirrors that give you views from different angles.

I've found that the side view is the most disastrous. With me, I'm usually reminded to keep my stomach sucked in for the rest of the day.

Mirror images can be disconcerting. Why, for instance, do mirrors reverse an image across the vertical axis of symmetry from left-to-right, but not up-and-down? On the other hand, a person standing on a mirror floor would observe objects in the room with left and right unchanged, but reflected across the horizontal axis of symmetry--in other words, upside down.

Many capital English letters have axes of symmetry. Some have horizontal axes of symmetry, some vertical, and a few--H, I, O and X--have both. To illustrate, print the names TIMOTHY and DICK on a piece of paper, both in vertical columns and horizontally. When a mirror is held above the vertical columns and viewed from the top of the column, TIMOTHY appears unchanged, but DICK is reversed (with the exception of the letter"I", which also has a vertical axis of symmetry). Similarly, holding the mirror above the horizontally written names and viewing from below, DICK appears unchanged, but TIMOTHY is upside down and mirror-reversed. The reason, of course, is that all the letters in TIMOTHY have vertical axes of symmetry, and all those in DICK have horizontal axes of symmetry.

Almost everyone has noticed that if they look into a corner that has mirrors abutting at right angles, their face looks a little strange. If you blink your right eye, the image in the mirror(s) blinks its right eye also--but it's the "real" right eye on the opposite side of what you're accustomed to when you look into your bathroom mirror. In a plane mirror, if you blink you right eye, the guy on the other side seems to blink his left eye.

But in the double mirror, the light has been reflected twice by the two mirrors in the corner, and not just bounced back once from a plane mirror, in which the image is reversed. In other words, the image has been re-reversed and appears as it normally would to a person standing in front of you.

In the corner mirror, your face will probably look strange to you because, although most faces are reasonably symmetrical, there are enough minor differences between the left and right hand sides to make them slightly different. While the one that you see in the mirror every morning is the person that you think you know, the one in the corner mirror is what the rest of the world sees.

It's instructive to play this game by yourself. Just get two small mirrors and place them so that their surfaces are at right angles, with their common edge vertical (it helps to use a piece of tape on the back). Look into them at an angle midway between the two mirror faces. You may not recognize yourself right off, but that's you.

For the clincher, hold the mirrors so that their common edges are horizontal. What you see now is still an unreversed image of what you really look like, but you're upside down!