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Why do mirrors flip things horizontally (but not vertically)?

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When you look in a mirror, you’re looking at a horizontally backwards
version of yourself, right? Wrong. As the Physics Girl explains, it’s
more complicated than that.

Mirror image is a tricky thing, but it’s pretty clear when you look
at words in a reflection, that mirrors flip things horizontally rather
than vertically. Or, at least it seems that that’s the case.
 
For
example, when you hold up a sign saying “Food” in the mirror”, it flips
reads a backwards “dooF”, but the letters are still the right way up.
And why, when you raise your right hand, your mirror-self raise its left
hand, but it still moves it up rather than down. How does a mirror know
the x direction from the y direction?
In this episode,
the Physics Girl explores what’s going on. Because, you see, the reason
that things appear to always be flipped horizontally in the mirror is
because we flip them horizontally. 
Try holding up that
“Food” sign again, but then flip it vertically to face the mirror, and
then you’ll see an upside down, but forward facing, “Food” staring back
at you.

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The reality is that the mirror isn’t flipping things
horizontally or vertically at all, it’s actually flipping them along the
z direction – the one that points out in 3D from a traditional graph.
You can see this illustrated in the video.
That might sound
confusing, because it’s hard for us to visualise the z direction when
we’re so used to seeing things along horizontal or vertical axes – and
because we’re horizontally symmetrical, we don’t notice that things
aren’t truly horizontally flipped when we look in the mirror.
But the Physics Girl does an amazing job of explaining it in the video below
with a left-handed glove. To see how it would look in a reflection, you
would need to peel that glove off and turn it inside-out. That’s the true mirror image – no horizontal flipping required.
Of course, that doesn’t make much sense until you see it for yourself. So watch the episode and be prepared to never look at your mirror-self the same way again.

Source: Physics Girl

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