Searching for a nice explanation: Plane Mirror

[DaTario]

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

 

[mathman]

It is simply a definition question. Suppose you look at a mirror while lying down on your side. Then the exchange will be top and bottom and not right and left.

 

[harrylin]

It is simply a definition question. Suppose you look at a mirror while lying down on your side. Then the exchange will be top and bottom and not right and left.

Right. A little more elaboration: it is a very strong suggestion due to a combination of two factors:

1. the (almost) left-right symmetry of faces
2. gravity

As a result your face in the mirror looks like a person who has turned around a vertical axis by 180°, as we are used to. If you do the same with for example playing cards then you can turn it also around the horizontal axis and the illusion is gone.

 

[DaTario]

It is simply a definition question. Suppose you look at a mirror while lying down on your side. Then the exchange will be top and bottom and not right and left.

Still the image of this person will experience an exchange between his left and right. The corresponding experiment in which the person remains still and the mirror rotates 90 degrees shows no apparent modification as well.

 

[DaTario]

Imagine a face of being as a compact disc with four marcs of different colors located at the edge: blue for (our) up, red for (our) down, green for (our) left and yellow for (our) right. Let his eyes be unique and located at the center of the disc. Once he is right in front of some plane mirror what should be his testimony. Will he declare that the image has only exchanged green and yellow?

Best wishes

DaTario

 

[mfb]

A mirror exchanges "front" and "back". If you rotate a human by 180° along its vertical (head<->feet) axis and exchange "front" and "back" afterwards, it is similar to an exchange left<->right. But that is an arbitrary way to handle directions, to make the feet pointing "down" again.

If something in the mirror appears to be above/below your head, the object will be above/below your head.
If something in the mirror appears to be left/right of your head, the object will be left/right of your head.
Do you see the symmetry?

 

[harrylin]

Imagine a face of being as a compact disc with four marcs of different colors located at the edge: blue for (our) up, red for (our) down, green for (our) left and yellow for (our) right. Let his eyes be unique and located at the center of the disc. Once he is right in front of some plane mirror what should be his testimony. Will he declare that the image has only exchanged green and yellow?

Best wishes

DaTario

Sorry that doesn't make sense to me in view of my explanation in post #3 (to which you did not respond). For symmetry you would need to put 4 eyes; else it is you who makes the effect. Or you could try with drawing one eye above, and one eye beneath!

 

[jtbell]

Why a plane mirror image exchanges right with left but does not interfere with up and down?

See the attached picture. Are left and right exchanged between the plastic sheet and its reflected image?

 

[harrylin]

See the attached picture. Are left and right exchanged between the plastic sheet and its reflected image?

Nice one!
(Is that you?)

 

[A.T.]

A mirror exchanges "front" and "back". If you rotate a human by 180° along its vertical (head<->feet) axis and exchange "front" and "back" afterwards, it is similar to an exchange left<->right.

This is the key, to the confusion. The brain is used to assume rotations, not mirroring. So given certain symmetries it wrongly assumes that the mirror image is rotated by 180° along a certain axis, rather than just mirrored at the plane. This assumed rotation makes it then difficult to interpret what was exchanged by the mirror.

https://www.youtube.com/watch?v=msN87y-iEx0

 

[mathman]

Right. A little more elaboration: it is a very strong suggestion due to a combination of two factors:

1. the (almost) left-right symmetry of faces
2. gravity

As a result your face in the mirror looks like a person who has turned around a vertical axis by 180°, as we are used to. If you do the same with for example playing cards then you can turn it also around the horizontal axis and the illusion is gone.

Gravity has nothing to do with it.

 

[mfb]

Gravity influences the way our brain interprets images. See the video in the post above for an explanation.

 

[A.T.]

Gravity has nothing to do with it.

That's true. Creatures living in zero-g and having a plane symmetrical body like humans would have the same confusion.

 

[jtbell]

Nice one!
(Is that you?)

Part of me, anyway.

 

[DaTario]

Sorry that doesn't make sense to me in view of my explanation in post #3 (to which you did not respond). For symmetry you would need to put 4 eyes; else it is you who makes the effect. Or you could try with drawing one eye above, and one eye beneath!

Sorry for not responding. I was trying to focus on contributions upon which I could elaborate more. But thank you a lot. I believe that the number of eyes has no determinant role to play in this discussion.

Best wishes,

DaTario

 

[DaTario]

See the attached picture. Are left and right exchanged between the plastic sheet and its reflected image?

If the L letter you draw was a man, he will understand its image as facing him with the left-right exchanged. But now I guess we here touched a fundamental point. Mirrors provide front-back exchange. This effect can be presumed by the symmetry the plane have. And this front-back interplay yields this interpretation of left-right exhange.

In terms of a nice explanation, I guess we are pretty near.

Best wishes,

DaTario

 

[DaTario]

This is the key, to the confusion. The brain is used to assume rotations, not mirroring. So given certain symmetries it wrongly assumes that the mirror image is rotated by 180° along a certain axis, rather than just mirrored at the plane. This assumed rotation makes it then difficult to interpret what was exchanged by the mirror.

https://www.youtube.com/watch?v=msN87y-iEx0

Very nice. I my self recognized this video as the source of my question here. I was not remembering from where I took this question. For a moment I thought I have reached this problem independently, but I watched this video a couple of years ago and now I guess the problem is solved to me. Thank you.

Best Regards,

DaTario

 

[harrylin]

Sorry for not responding. I was trying to focus on contributions upon which I could elaborate more. But thank you a lot. I believe that the number of eyes has no determinant role to play in this discussion.

Best wishes,

DaTario

I also believe that the number of eyes has no determinant role to play in this discussion. 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. If you do the same with for example playing cards then you can turn it also around the horizontal axis and the illusion is gone. However, it seems that somehow you suddenly understood it.

 

[jtbell]

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.]

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]

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]

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]

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.]

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:

https://www.youtube.com/watch?v=2FyrJEhnENg

 

[robinpike]

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.