Can a single plane mirror flip things vertically?

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It doesn't flip things vertically or horizontally but in the third dimension - front to back. The confusion arises because humans have bilateral symmetry. If you imagine your nose passing through your head, and your toes through your heels to produce the reflection, and everything else doing likewise, then you will produce in the imagination the reflection exactly. But what one tends to imagine is that one slides around into the mirror and turning to produce the reflection, which seems to work horizontally because of the body symmetry, but if you imagine the same movement vertically one is upside down, because the lack of symmetry does not allow one to imagine that head has become feet, whereas the symmetry of the body does allow one to imagine that left has become right.

The answer to this question is surprisingly simple.

Yes, a single plane mirror can flip things vertically.

Place the mirror flat on the floor like a rug. Step onto the mirror being careful not to break it.

You can now look down and you will see an image of yourself flipped vertically.

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Quoting Deleted user

It's... still not flipped vertically.

The head of the image is below the feet. How is that not flipped vertically?

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Quoting Agree-to-Disagree

Place the mirror flat on the floor like a rug

Quoting Deleted user

It's... still not flipped vertically.

Yea, A2D, what were you thinking? It's goes on the ceiling, duh! Putting on the floor requires you to step on it and break it.

Quoting Deleted user

To flip something vertically means to draw a horizontal line in the center, and take everything in coordinate +1 and put it in -1, +2 to -2, and so on, now take -1 and put it in +1, -2 to +2, and so on.

How does putting the mirror on the floor not do exactly that (assuming x axis is vertical, usually it is y or z by convention).

A concave mirror (on the wall, sufficiently distant) rotates the image 180 degrees, and still flips it front to back, not top to bottom.

Quoting unenlightened

It doesn't flip things vertically or horizontally but in the third dimension - front to back. The confusion arises because humans have bilateral symmetry.

In other words, what we see in a mirror is an optical illusion? Does the brain try to make sense of the symmetry flip, by imagining the third dimension inverted? :joke:

Quoting Gnomon

In other words, what we see in a mirror is an optical illusion?

Assuredly not! As this paper by a famous mathematician demonstrates.

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Quoting unenlightened

In other words, what we see in a mirror is an optical illusion? — Gnomon
Assuredly not! As this paper by a famous mathematician demonstrates.

So, Lewis Carroll proved that what we see in the "looking glass" is actually a separate dimension where everything is reversed from the normal world. Now it all makes sense. :joke: