Michael Mason says:

I did a casual duplication of the experiment on my coworkers, and it's great fun. It's all true of course--we just used pieces of tape to mark head size in the mirror, and walked back and forth, marvelling at the results.

Mark Hadfield says:

There's a better way of understanding all this. (By better, I mean more coherent and more in line with simple physical theory.) When you look at yourself--or any other object--in the mirror the image is not at the mirror surface it's behind it, exactly as far behind the plane of the mirror as the actual object is in front. It's called a virtual image because no light rays actually go through it.

And that, of course, is exactly what it looks like. Ask any cat who has tried to fight with its reflection. A mirror looks like a window through which you can see another world, one in which all the objects seems to be strangel reversed versions of the objects in your world.

Your observations about tape on the mirror surface follow from this (well, OK, I'd never actually worked out this bit of it for myself) but they miss the point somewhat. The image of your head is not at the mirror surface! Putting tape on the mirror is a bit like putting tape on a window when you're looking at an object outside.

Put a mark on a mirror and then stand fairly close to the mirror and focus on your face. Is the mark in focus? No.

My qualifications to say this: I have a PhD in physics, but I learnt this stuff in high school. I remember finding it pretty weird for a while, just as I found a lot of other physics weird. But it works! It's the reason I love physics so much.

Mark Hadfield says:

I got around to reading the paper. I've quoted the first paragraph of the introduction below.

It seems to me that the authors and the Gombrich they cite could have done well to pay more attention in high school physics. "The image on the mirror surface" indeed!

Quote:

There is a famous passage in Gombrich's (1960, p. 5) classic book Art and illusion about the perception of our own head in mirrors. Gombrich points out that we see ourselves in mirrors without any conscious awareness of the size of the image on the mirror surface. He suggests a little demonstration on the fogged up mirror of our bathroom. If we circle the outline of our own head we will be amazed to discover that it is much smaller than our head. Indeed, it is exactly half independently of distance. To Gombrich, this is an example of an illusion in the sense that we are only aware of seeing ourselves face to face and we stubbornly refuse to see the size on the mirror surface.