Science Puzzle
Why Does a Mirror Swap Left and Right?
Stand in front of a mirror and raise your right hand. Your reflection seems to raise its left. Writing on your T-shirt appears back to front. Yet the mirror never turns you upside down: your head stays at the top and your feet at the bottom.
How can a flat mirror swap left and right but not up and down, when it treats every direction along its surface the same?
The Answer
It doesn't swap left and right at all. A mirror swaps front and back. The left-right swap is something your brain adds.
Look at Fig. 1 again. Your raised hand is on the right-hand side of the picture, and so is the reflection's raised hand. Nothing has moved sideways. Up stays up, the hand on the window side stays on the window side. The only direction that changes is the one straight into the mirror: point at the mirror and your reflection points straight back at you. The mirror has reversed front and back.
So why does it feel like left and right? When you look at your reflection, your brain treats it as another person facing you. To face you, a real person would have to walk round and turn about. People turn round about an upright line, the way we always do, and that turn swaps their left and right while keeping their head on top. Comparing the reflection with that imaginary turned-round person, the hands seem to have swapped. If we were in the habit of flipping head over heels to face each other, we'd say mirrors swap up and down instead.
The writing on your T-shirt is the same story. It looks reversed because the T-shirt faces the mirror, front to back, not because the mirror has a favourite direction.
The principle: A mirror reverses the direction at right angles to its surface, front and back, and nothing else. The apparent left-right swap comes from comparing the reflection with a person who has turned round to face us.