Why Does a Mirror Reverse Left and Right?

Stand in front of a mirror and raise your hand. You raise your right hand, but the person in the mirror appears to raise their left. Text appears reversed left-right in mirrors too.

But this is strange. Why does the mirror only reverse left-right but not up-down? If a mirror can flip left-right, shouldn't it flip up-down too?

The common answer: "mirrors have the property of reversing left-right" — or "humans are left-right symmetric, so the reversal is more noticeable on that axis." Sounds plausible. But this isn't the real essence.

Actually, a mirror reverses neither left-right nor up-down. A mirror reverses only one thing: front-back (z-axis, depth). If you stand 1m in front of the mirror, your image appears 1m behind it. The x-axis (left-right) is unchanged. The y-axis (up-down) is unchanged. Only the z-axis (front-back) flips.

So why do we feel "left-right reversal"? Answer: because we mentally imagine the mirror image as a "person who has turned around to face us." For a real person to face us from the mirror's position, they would need to rotate 180° around the y-axis (vertical axis). This rotation swaps left and right. So "left-right reversal" is not the mirror's doing — it's the result of mental rotation in our minds. If we instead rotated around the x-axis — i.e., looked at a mirror while upside down — the image would appear "up-down reversed." The mirror is the same; only our perception changes.

→ The mirror flips neither left-right nor up-down — only front-back. Left-right reversal is just our perceptual convention.

When the real person on the left raises a hand, the image beyond the mirror appears to raise the opposite hand, mirror-symmetric across the glass (the dashed line links the same hand). Look at the axes: the x-axis (left-right) and y-axis (up-down) stay put, and only the z-axis (front-back) flips — step 2 highlights the z-axis in red. The rotation panel in step 3 shows that to turn the mirror image into a "person facing you," you must rotate the body 180° around the y-axis, and it is that rotation that swaps left and right. Step through it yourself with the buttons.

Use the step buttons (1·2·3) to walk through observation → z-axis flip → 180° rotation. Hover an axis to highlight it.

[Ambulances] "ƎƆИAJUᙠMA" painted on the hood — so the driver behind reads "AMBULANCE" correctly through their rearview mirror. The mirror's z-axis flip appears to us as "left-right reversal."

[Selfie camera mirror mode] Phone selfies are mirror-mode by default (left-right reversed display). We're used to seeing ourselves in mirrors, so non-mirror photos feel strange.

[Ceiling mirror] Look up at a ceiling mirror and the image appears up-down reversed. This time you've tilted your head around the x-axis, so the same z-axis flip is perceived as "up-down reversal." The mirror itself is unchanged.

[Offset printing] Printing plates have text engraved in mirror image (left-right reversed). When pressed to paper, the z-axis flip produces normal text. Same principle as the mirror.