Henry Dumbleton, a homeschooler of Lyttelton, asks :-

Why does a reflection in a mirror reflect left to right and not up to down?

John Campbell, a physicist at the University of Canterbury, responded.

We see ourselves in a mirror because light is scattered off our body and reflected into our eyes. Because of the reflection we see an image of ourselves at the same distance behind the flat mirror as we are in front of it. The image of our head is above our eyes and our feet below. The image of our right arm is to the right hand side of the image we see.

We interpret this image as us standing behind the mirror and facing ourselves. So we interpret the right hand side of the image as our left arm. But it isn't. Show this by moving your right arm up and down. The arm on the right of the image moves. Because we normally wear clothes that are symmetric like our body we interpret this as the left arm of the image moving. If we normally wore clothes where one sleeve was a different colour to the other, for example as in some practice rugby shirts, we would be less likely to fall for this illusion.

If you have two mirrors set them vertically but at right angles to each other and touching along one edge. Now move one arm. Which one in the image moves? And where does the image of your eye always appear to be?

Also, bearing in mind that light rays travel in straight lines and the angle of reflection equals the angle the ray is incident onto a flat mirror, can you draw a diagram that shows that a mirror in which you wish to see the whole of your body need only be half the length of those sold as full length mirrors?