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Searching for a nice explanation: Plane Mirror

by DaTario
Tags: explanation, mirror, plane, searching
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jtbell
#19
Oct29-12, 08:26 AM
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To see more clearly where the usual left-right reversal in a mirror image comes from, first note that in my picture, the letters are written on the side of the plastic sheet that faces me. Now imagine replacing the clear plastic with cardboard. We no longer see the letters in the mirror because they're on the "wrong" side of the sheet, facing away from the mirror.

To make the letters visible in the mirror, we need to flip the sheet around. If we flip the sheet horizontally (around a vertical axis), we see the usual "mirror-reversed" image. What happens if instead, we flip the sheet vertically (around a horizontal axis)?
A.T.
#20
Oct29-12, 08:33 AM
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Quote Quote by harrylin View Post
I explained that your face in the mirror looks like a person who has turned around a vertical axis by 180, as we are used to.
I think that even with a completely asymmetrical object, the brain still tries to interpret it as rotation first. It's just what it does all the time when your eyes are open, and you recognize familiar objects from different angles. Recognizing mirrored objects is used less.
harrylin
#21
Oct29-12, 09:05 AM
P: 3,187
Quote Quote by A.T. View Post
I think that even with a completely asymmetrical object, the brain still tries to interpret it as rotation first. It's just what it does all the time when your eyes are open, and you recognize familiar objects from different angles. Recognizing mirrored objects is used less.
The point that mathman, mfb, jtbell and I made was that we have a preference for horizontal rotation. I added that by chance that matches facial symmetry so that the illusion is enhanced.
Anyway, everything has been explained several times now.
hog
#22
Oct30-12, 10:16 PM
P: 5
New here :-) a mirror reflects light. It does not reflect psychology .. up, down, right, left has no definition outside of human behavior. I see that as the biggest problem in physics. Go find the right side of the earth .. the bottom of a star. Maybe the question is, "where does human behavior stop and physics begin?" In psych class one night, professor asked us to "calculate the statistical probability of a bird landing on a branch during a heavy storm." Long pause .... it's 100% ! The bird behaves. He doesn't care about physics or math. And we're pretty good with mirrors.
DaTario
#23
Nov2-12, 03:09 PM
P: 555
Trying to summarize:

The operation that is implemented by the mirror on the system of light rays which emerge from an object may be called mirroring and has to do with a front-back inversion. As this operation is mechanically unpractical, our brains tend to interpret it as a rotation around a vertical axis followed by an inversion left-right. Mathematically we may see it from the equivalence between two procedures:

1) (x , y , z) -> (x , -y , z) reflection in the xz-plane.

2) (x , y , z) -> (-x , -y , z) rot 180 around z-axis followed by

(-x , -y , z) -> (x , -y , z) reflection in the yz-plane (exchange of left and right)

Best wishes,

DaTario
A.T.
#24
Nov18-12, 07:22 AM
P: 4,078
Quote Quote by DaTario View Post
Trying to summarize:

The operation that is implemented by the mirror on the system of light rays which emerge from an object may be called mirroring and has to do with a front-back inversion. As this operation is mechanically unpractical, our brains tend to interpret it as a rotation around a vertical axis followed by an inversion left-right. Mathematically we may see it from the equivalence between two procedures:

1) (x , y , z) -> (x , -y , z) reflection in the xz-plane.

2) (x , y , z) -> (-x , -y , z) rot 180 around z-axis followed by

(-x , -y , z) -> (x , -y , z) reflection in the yz-plane (exchange of left and right)
Made an animation to visualize this:

robinpike
#25
Nov19-12, 07:56 AM
P: 41
Quote Quote by DaTario View Post
Hi All,

The question is rather simple: Why a plane mirror image exchanges right with left but does not interfere with up and down?

Best wishes,

DaTario
Hi DaTario,

What the mirror does is the same as writing in wet ink...
. Top
.Left Right
. Bottom
on a piece of paper, say stuck on a wall in front of you, and then getting a friend to put another piece of paper on top of the still wet writing and then they move that paper away from the wall, without that person turning the paper in any way.

Now if you turn your head from looking at the paper on the wall, to the one your friend is holding (the mirror image), you will see Left and Right switched, but Top still at the top and Bottom still at the bottom.

However, you could also look at the piece of paper your friend is holding by bending down and looking through your legs. If you were to do this, then you would see Bottom at the top and Top at the bottom, with Left still on the left, and Right still on the right.

As we normally just turn our heads when looking at a mirror image (rather than look through our legs), we see left and right switched, and top and bottom staying as they are.


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