A while back I wrote how you get lateral inversion (“mirror writing”) in a mirror.  I worked out the solution independently of the (same) one given by Martin Gardner in his book “The Ambidextrous Universe”.  I was so proud of myself that I also included a demonstration of how a mirror works in my Inaugural lecture as a new Professor – it’s a good job there were no bright kids in the audience.  Today I got this e-mail from a schoolteacher, which is also included as a comment in the original post.

Elizabeth Curtis says:
September 10th, 2008 at 9:25 am

In trying to teach physics in 7th grade, I found your explanation fabulous. My children began to discuss the reflection, say in a lake of tress and clouds and the lateral flip got mixed up with the upside down. Any comment or helpful suggestions. Thanx

I must admit I hadn’t considered the case of the mirror lying horizontally, and even if I had I don’t think I would have thought there’d be any difference.  Obviously the kids know better!  There are plenty of images of mountains reflected in lakes on the web – take a quick look now.  As is correctly mentioned in the above post there is not only a lateral inversion – but also a top-bottom inversion as well!  I need to go away and give this one some thought!  Probably a LOT of thought!!

Elizabeth – you have some very bright kids there, please send them over to do a PhD with me when they are old enough 🙂

Update!  I have just carried out some experiments with a mirror, and had a look at Martin Gardner’s “The Ambidextrous Universe” again.  In fact Martin does discuss the up-down inversion with horizontal mirrors (above or below the object) – but this is NOT the whole story.  The situation has an added complication with the horizontal mirror, is the object on the same edge as the mirror as you (the observer) or beyond the far edge (away from you).  I will need to resort to the letters written on transparency to see if I can figure out what’s going on here – but it is a lot more complicated (to explain) than simple lateral inversion where the object faces the mirror and you (the observer) are directly behind the object.

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