How it works
When people imagine standing in a reflection’s place, they mentally rotate themselves around a vertical axis, which swaps left and right. Rotating over a horizontal axis would instead appear to swap top and bottom.
What people often miss
Writing looks reversed because the reflected page faces the opposite direction, not because the mirror has a preference for horizontal directions.
Why this question comes up
The everyday phrase mirror image hides a surprisingly subtle geometry question.
Key points
- A mirror does not specifically swap left and right. It reverses the direction perpendicular to its surface, turning front toward back in the reflected coordinate system.
- When people imagine standing in a reflection’s place, they mentally rotate themselves around a vertical axis, which swaps left and right. Rotating over a horizontal axis would instead appear to swap top and bottom.
- Writing looks reversed because the reflected page faces the opposite direction, not because the mirror has a preference for horizontal directions.
Bottom line
A mirror does not specifically swap left and right. It reverses the direction perpendicular to its surface, turning front toward back in the reflected coordinate system.
Source and verification
This Answer was checked against Exploratorium: Mirror Reversal. Follow the source for the full official explanation and any later updates.