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.
My friend K. emailed this to me & some friends, with the following addendum: “I am intrigued by this half step rule, but every time I go to the mirror to stare at my face and try to test it out I get so distracted by how good my hair is looking today (just the right level of humidity) and how clear my skin is (born with it) and how sparkling my eyes are (it’s true!) and just how darned pretty I am that I forget to be scientifical. So can one of youse guys try it and tell me if it works?”
Special to K: it does work. I just tried it, using a bar of soap to outline my little face. Now I’m madly Googling “How to get soap off the bathroom mirror”. Thanks.