The Curiosity Shop

Mirror Image Reversal

I think a simple explanation of the mirror stuff is this. If you are facing north facing a mirror, the image of your head is still toward the sky, the image of your feet at the ground. The image of your right hand is still toward the east and your left toward the west. The only thing that is different is the image of your front and back. yar face north but the image of you faces south. Mirrors only change the direction of "forward". This one change reverses the "handedness" of the coordinate system that is reflected, to put it mathematically. Right-handed systems are reflicted as left-handed and vice versa. Any time you reverse the handedness it causes writing to appear backwards and clocks to go in the opposite direction.

There are two types of directions involved here, those that do not depend on the orientation of the observer and those that do. Imagine a person facing north, say, looking in a mirror. If he raises his eastern hand the mirror image will raise its eastern hand. If he points his finger toward the sky the mirror image will do the same. Skyward and east are defined without respect to the observer. The mirror does not change them.

On the other hand 'forward' is a direction very dependent on the observer. If he moves it changes. A mirror changes 'forward'. It reverses it. What is forward for the observer is backward for the image. That's because the image faces in the opposite direction from the observer.

What is perhaps less obvious is that left and right are dependent on the directions up (i.e. toward the observer's head) and forward. If these change so too do the directions "left" and "right" More simply put, if the observer moves, right and left move with him. If the observer turns 180 degrees what was to his left is now to his right. That is true both if his turn is so as to reverse forward and backward or so as to reverse his up and down.

Now when the observer looks in a mirror his head is presumably skyward and the mirror reflects that. The mirror, in its reflection, turns forward around 180 degrees, however. Right and left, in the reflection, are therefore turned around also, just as if the observer had turned around 180 degrees. That's all there is to it. Change the direction "forward" and you change which direction is to the right and which is to the left.

In April I got the following email from a reader dissatisfied with the explanation above:

Subject: Mirror question
Date: Thu, 15 Apr 1999 22:39:58 -0400
From: John C

Your answer to the mirror puzzle is quite insufficient.  What is written
reveals an acute misunderstanding of the question.


This lead to an interesting exchange of emails that you may find enlightening.

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