It sounds like this“A mirror flips left and right, but not up and down.”
Thinking a mirror swaps left and right
Why it feels right
It is what everyone says, and it is what we seem to see. Raise your right hand and the reflection raises the hand that looks like its left. Hold up a book and the writing is back to front sideways, not upside down. A mirror that picks out left and right and leaves up and down alone looks like a strange rule, which is why people have asked about it for centuries.
Why it’s wrong
A mirror reverses only front and back, the direction straight at the glass. Your left hand is still on the left side of the room in the reflection, and your head is still at the top. Left and right only look swapped because we picture the reflection as a person who has turned round.
A worked example
Look at the geometry. A mirror is a flat plane. A point 40 cm to your right, 100 cm up and 60 cm in front of the glass has an image 40 cm to the right, 100 cm up and 60 cm behind the glass. Sideways and up stay the same; only the distance from the glass changes sign.
So the mirror hasn't flipped left and right at all. Stand with your right hand toward the east wall: the reflection's matching hand is also toward the east wall. Your head is up and so is its head. The only direction that swaps is the one pointing at the mirror: your nose points at the glass, and the nose of your image points back out of it.
Why does it seem like a left-right swap? We read the reflection as if it were another person facing us. To face you, a real person would have turned round, and turning round swaps the left and right hands. The mirror image has not done that: it has been turned inside out front to back. Comparing it with a person who turned makes the difference look sideways.
How to catch yourself
- You say a mirror 'flips left and right'.
- You wonder why it is left and right and not up and down.
- You expect a mirror on the ceiling to flip something different from one on the wall.
What to hold instead
A mirror reverses only the direction at the glass, front to back. Sideways and up stay where they are. Left-right looks swapped only because we compare the image with someone who has turned round to face us.
Where you’ll meet it
- Wondering why text looks back to front in a mirror.
- Seeing why your parting looks on the wrong side in a selfie.
- Explaining why a mirror does not turn things upside down.
Questions people ask
- Does a mirror really flip left and right?
- No. It flips front and back, the direction perpendicular to the glass. Left and right stay on the same sides of the room. The impression of a left-right swap comes from imagining the reflection as a person who has turned around.
- Why doesn't a mirror flip things upside down?
- Because up is parallel to the glass, so it is not reversed. Only the direction pointing into the mirror is reversed, so an upright person stays upright and only the front-to-back direction is swapped.