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Why does a mirror flip left and right but not up and down?

Mirror's Honest Trick
Why does a mirror flip left and right but not up and down?
Stand in front of a mirror and wave your right hand. Your reflection waves back — ~~but it's waving with the hand on YOU

Stand in front of a mirror and wave your right hand. Your reflection waves back — but it's waving with the hand on YOUR right side, which looks like THEIR left hand. It's like your mirror twin is backwards. So why does the mirror flip you sideways but not upside-down? Your head's still on top, your feet still on the bottom. What's going on?

Here's the trick: the mirror isn't actually flipping left and right at all. What it's REALLY doing is flipping front and back. The mirror takes whatever's closest to it and reflects it back as closest, and whatever's far becomes far in the reflection. It's a DEPTH flip, not a sideways flip.

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