Half the size of my head...

WAY back on July 22, The New York Times published an article about mirrors. It wasn't very good. This paragraph should give you a sense of what the article was about and, at the same time, how confusing it was.

With their capacity to reflect back nearly all incident light upon them and so recapitulate the scene they face, mirrors are like pieces of dreams, their images hyper-real and profoundly fake. Mirrors reveal truths you may not want to see. Give them a little smoke and a house to call their own, and mirrors will tell you nothing but lies.

Uhh, pieces of dreams? From there the article discusses how mirrors are helping scientists understand self awareness and how it influences our behavior.

But, if you had the patience to soldier through, there were a couple of cool, counter-intuitive tidbits about mirrors and the reflections we see.

For example, there are just a few non-human species that have been found to recognize themselves in a mirror - chimpanzees, bonobos, orangutans, gorillas, dolphins and Asian elephants. Interestingly, all animals that live in extremely sophisticated social groups.



Even cooler, consider this: Imagine you are standing in front of a bathroom mirror; how big do you think the image of your face is on the mirror?

About life size, wouldn't you say? More or less the same size as your own face and head.

And what would happen to the size of the reflected image if you moved farther and farther away from the mirror?

It would shrink right? As you move farther away from the mirror, the reflection of your face gets smaller.

These are the most intuitive answers but the fact is, the reflection of your face is exactly half the size of your actual face. Exactly half. And it's exactly half the size no matter where you stand. Get up close and it's half the size. Walk back and back and back and it's always half the size of your actual face.

The reason for this is that no matter how close or how far you are from the mirror, the mirror is always half way between your real self and the reflected you.

But wait. There's more.

This "rule of half" only applies to you. If you stand still in front of the mirror and a friend approaches, the size of the reflection of their face will grow larger! And if they back away, their reflection shrinks!

The article suggests...

...imagining that you had an identical twin, that you were both six feet tall and that you were standing in a room with a movable partition between you. How tall would a window in the partition have to be to allow you to see all six feet of your twin?

The window needs to allow light from the top of your
twin’s head and from the bottom of your twin’s feet to reach you. These two light sources start six feet apart and converge at your eye. If the partition is close to your twin, the upper and lower light points have just begun to converge, so the opening has to be nearly six feet tall to allow you a full-body view. If the partition is close to you, the light has nearly finished
converging, so the window can be quite small. If the partition were halfway between you and your twin, the aperture would have to be — three feet tall.

Optically, a mirror is similar except that instead of lighting coming from your twin directly through a window, you see yourself in the mirror with light from your head and your feet being reflected off the mirror into your eye.

Got that? Thankfully they included this helpful graphic.



The lesson is that the tools that we use to perceive the world have limitations. What we think we see and what we think we know aren't always real. Magicians regularly take advantage of these limitations. So do psychics. Seeing it with your own two eyes doesn't always make it so!