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Mirror Images

Written March 2009


Timmy stood with his back to the wall.  He picked up his name tag, the one that read TIMMY.  He peeled off the protective backing paper and attached the tag to the front of his shirt.  Did it look all right?  He turned around so that he could see himself in the mirror on the wall.

Timmy raised his right hand with a question.  “In the mirror, my name tag says YMMIT.  Why is that?  And why does my reflection have its left hand raised?”

More generally, why does a mirror swap things left-for-right?

And, come to think of it, why it does it not swap things top-for-bottom?  Why should the X dimension behave differently from the Y dimension?

When I was a college sophomore, I explained the conundrum this way (minus the illustration) in answering a physics textbook question about optics on April 28, 1967:

Actually, a mirror doesn't “reverse” anything; it's all in our definitions.

Consider a person facing west with a mirror in front of him.  His image appears to be facing east.  He raises his north hand; his image raises its north hand.  We call north “right” when we're facing west and “left” when we're facing east, so the person raises his right hand and his image raises its left hand.  But “raising” is defined as moving upward no matter which way you're facing, so the hand of both the person and his image moves up.

The dimensions don't behave differently, of course.  But we interact with them differently.  It all comes down to gravity and the way we stand on this planet.

If we want to turn around, it's easier to rotate our bodies this way (keeping our feet beneath us) than this way (turning ourselves upside down).

Who swapped Timmy's name tag left-for-right?  The mirror didn't do it.  Timmy did it himself, by pivoting from his left to his right with his name tag attached.  When he turned to face the mirror, he did it the easy way, rotating like this .

He could have done it the hard way and turned from top to bottom.  To do so, he would have had to lower his head to the floor so he was looking between his legs at the mirror, then stand on his hands with his feet in the air.  That would have been much more difficult. 

(Irrelevant digression:  If Timmy does want to reverse his reflection top-for-bottom, there’s a way to do it without inverting himself 180°.  All he has to do is move the mirror 90°.  If he takes the mirror off the wall, lays it face-up on the floor, stands on it, and looks down at it, he will observe his reflection standing on its head.  The soles of his reflection’s feet are uppermost, just below the soles of his real feet.)

Actually, a mirror doesn’t reverse things either left-for-right or top-for-bottom.  It reverses things front-for-back!

See, here I’m holding up a cutout of the letter R so that I can look at it.

And now I’m holding it in front of a mirror.  The reflection is showing me the backside of the letter instead of the front.  Notice this:  the reflection is not reversed left-for-right!

But if I flip the letter, turning it 180° about a vertical axis so that I can attach it to my shirt,  I’m now standing on the backside of the letter, with the sticker facing me. The reflection of its front side in the mirror seems to be reversed.

However, the mirror hasn’t flipped the letter around.  I have.

The reversal, dear Timmy, is not in our mirrors but in ourselves.



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