Mirrors are Counterintuitive

Imagine you are standing in front of a bathroom mirror; how big do you think the image of your face is on the surface? And what would happen to the size of that image if you were to step steadily backward, away from the glass?

People overwhelmingly give the same answers. To the first question they say, well, the outline of my face on the mirror would be pretty much the size of my face. As for the second question, that’s obvious: if I move away from the mirror, the size of my image will shrink with each step.

Both answers, it turns out, are wrong. Outline your face on a mirror, and you will find it to be exactly half the size of your real face. Step back as much as you please, and the size of that outlined oval will not change: it will remain half the size of your face (or half the size of whatever part of your body you are looking at), even as the background scene reflected in the mirror steadily changes. Importantly, this half-size rule does not apply to the image of someone else moving about the room. If you sit still by the mirror, and a friend approaches or moves away, the size of the person’s image in the mirror will grow or shrink as our innate sense says it should.

From the New York Times.

It’s been years since I studied the physics of reflection—I was never much of a physicist anyway—and when I have time it would be fun to puzzle this one out, but a quick test shows that the article is likely to be correct about both phenomena.

It’s fascinating that we can can so fundamentally misunderstand everyday objects like mirrors. Another way of thinking about this would be to say that it is fascinating that, hundreds of years after the discovery of mirrors and the physical and mathematical properties behind them, our education system is so poor that the vast majority of people—myself included—aren’t sufficiently familiar with the relevant science to be able to answer simple questions like these.


Written by multinormal

July 22, 2008 at 12:41 pm

Posted in Science

%d bloggers like this: