Can you trust the mirrors?

If one of your New Year's resolutions was to shape up, I have good news for you: You look much thinner than what you think you are. Don't believe me? Take an old lipstick or washable markers, stand in front of a home mirror and carefully draw your outline on a mirror. Now measure the size of the face you just drew. It would be about half of what you expected. Viva-la-mirror!


How can it be that you on a surface of a mirror is about half the size of the real you? Here is the math:


Take a look at the triangles ABC and DEC.
Your face and its virtual image in the mirror have a size AB. The projection of your face on the mirror surface is the red line DE. AB is twice the size of DE because CH is twice the size from you to the mirror.

Are you really half the size? No, I was just kidding.
Our brain focuses on what is reflected in the mirror, rather than on the surface of the mirror. AB and not DE.

This peculiar trick is from a great book by John D. Barrow "One Hundred Essential Things You Didn't Know You Didn't Know. Math Explains Your World."

Top image by Dru!, distributed under CCL.

22 comments:

  1. My parent have a mirror hung against the wall in their home at an angle against the wall. The top of themirror is a few inches from the wall, the bottom of the mirror hits the wall. It is a great set up, after looking at yourself one feels so tall and thin!

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  2. Also you're not right in front of the mirror so you're touching it. You're farther away so you'll look smaller in the mirror.

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