Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Trevorgronow on 28/11/2005 18:46:40
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I've been teaching physics for ages but I'm really struggling with a sensible explanation for why I'm back to front sideways in a mirror but not upside down - other than "it's like another person facing you" I've notgot a lot to say...can some imaginative person come up with something better for me please?
Trevorgronow
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Trevor,
you're a physics teacher? Oh goody, someone who can answer all our questions! [:D]
I like the mirror question - I've never thought about it that way before. In fact, it's so good it prompted me to spend ages searching the web for an answer.
It turns out it's a fairly well known question, with lots of web links attempting to answer it - mostly with punny titles like "Some reflections on the mirror problem" (oh dear, oh dear). But it's hard to find a single, definitive, definitely "correct" answer.
The best (in my opinion) three sites that I've found are as follows. Problem is, they're all a bit long. The first link below is probably the easiest to read. The first paragraph of the second link is useful too.
http://www.redrice.com/ci/mirrorProblem.html
http://www.mathpages.com/home/kmath441.htm
http://www.mathpages.com/home/kmath142.htm
As for how to summarise what these links are saying (in a way that your students would understand, say) ... well, I'll leave that for you to do as your homework.[}:)]
Paul.
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How about 'If you imagine the image yourself in the mirror being like a painting on a piece of glass, if you look at the painting from beyond it it will look the right way round, but to look at it from where you are standing you have to look at the back of the painting, so it is the wrong way round.'
In fact the direction you think everything gets swapped is actually an artifact of how you walk around the picture. If you rotated you and the room onto its side, and you walked around the picture (which would now look to you as if it were on its side) the feet and head would look like they had swapped. 3D rotations are wierd things.
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Thankyou Paul - see I think the number of web links to this indicate that it's not so simple as it might appear (especially if you have to explain it to other people). However, If you read my next reply you'll find a rather thought-provoking scenario. It amuses me no end to imagine how many people are walking round the room imagining they're circling a painting of themselves lying on its side...physics has never been such fun [:)]
quote:
Originally posted by Solvay_1927
Trevor,
you're a physics teacher? Oh goody, someone who can answer all our questions! [:D]
I like the mirror question - I've never thought about it that way before. In fact, it's so good it prompted me to spend ages searching the web for an answer.
It turns out it's a fairly well known question, with lots of web links attempting to answer it - mostly with punny titles like "Some reflections on the mirror problem" (oh dear, oh dear). But it's hard to find a single, definitive, definitely "correct" answer.
The best (in my opinion) three sites that I've found are as follows. Problem is, they're all a bit long. The first link below is probably the easiest to read. The first paragraph of the second link is useful too.
http://www.redrice.com/ci/mirrorProblem.html
http://www.mathpages.com/home/kmath441.htm
http://www.mathpages.com/home/kmath142.htm
As for how to summarise what these links are saying (in a way that your students would understand, say) ... well, I'll leave that for you to do as your homework.[}:)]
Paul.
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I think it may be because your eyes are on a horizontal plane
[:)]
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quote:
Originally posted by Bianca4289
I think it may be because your eyes are on a horizontal plane
(Mr Gronow's student)
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[xx(]
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quote:
Originally posted by Trevorgronow
quote:
Originally posted by Bianca4289
I think it may be because your eyes are on a horizontal plane
(Mr Gronow's student)
Don't own up to being my students you fool, you're supposed to be clever [V]
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quote:
Originally posted by TheNakedBottoms
[xx(]
Not even remotely scientific...
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This is a one of those classical problems that I find difficult to understand why people have so much trouble with.
The image in the mirror is not reversed. The image in the mirror is the correct image of yourself. It is your preconception of yourself that is reversed.
You expect yourself to look the same way as you see other people. The trouble is that when you see the face of another person, they have turned around to face you, and they have turned around by rotating around a vertical axis (they do this because they are standing on their feet – if they were to flip over a horizontal bar in order to face you, they would indeed seem to be upside down to your expectation of them).
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I think the problem lies in how we've all had it explained to us at school - you know, the angle of relection thing.
Think of it this way. The reflection of any given part of an object is directly in front of it. Therefore the reflection of your left arm is to your left, the reflections of your feet are at the bottom etc.
If you want to see the reflection of your left arm you therefore still have to look to your left and to see your feet you still have to look down.
The question I asked my physics teacher about this was slightly different. You must all have seen the classic illustration of this with little lines & arrows from parts of a person going to the mirror & hence to the eyes - the 1 that shows angles of reflection. What I wanted to know is why isn't the image we see the size of where those lines touch the mirror? In other words, if the light from our feet hits the mirror halfway between our feet & our eyes, why doesn't our reflection look only half as tall as we really are?
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quote:
the feet and head would look like they had swapped
So your head would be on the end of your legs & you'd have feet sticking out of your neck? [:o)]
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quote:
Originally posted by DoctorBeaver
I think the problem lies in how we've all had it explained to us at school - you know, the angle of relection thing.
Ah well, that explains it, I never listened much at school [:)]
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quote:
What I wanted to know is why isn't the image we see the size of where those lines touch the mirror? In other words, if the light from our feet hits the mirror halfway between our feet & our eyes, why doesn't our reflection look only half as tall as we really are?
Eth - your reflection IS only half as tall as you. Try looking at yourself in a full length mirror. While doing this, direct someone else to put a mark / stick tape on the mirror where you see the bottom of your feet and the top of your head. (Note: where you see these things, not where the other person sees them in the mirror.) Then go measure the distance between the two marks. You'll find that it's half your height!
(P.S. This assumes the mirror is exactly perpendicular to the ground and the ground isn't sloping, etc. Otherwise the distance between the marks may be less than half your height.)
Q.E.D.
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I wonder if the following helps anybody? (Well, it helps me anyway.)
This borrows heavily from the links I gave above, btw - especially the 3rd link.
Suppose you cut out a large letter 'p' (made from cardboard, say).
1. If you face a mirror and hold the letter up in front of you, you see the letter 'p' in the mirror, the right way round. So nothing is reversed.
2. Place the letter 'p' in front of you, then hold a mirror to your side (so that it's upright and at right angles to both you and the letter). Now look at the image of the letter in the mirror. You'll find it's no longer a 'p', instead it's a 'q'.
This works whether the mirror is on your left or on your right.
Reason: the image has been rotated around the vertical axis - i.e. the axis the mirror has been placed in (the mirror is "upright"). So you get the perception of 'left-right' reversal.
3. Place the letter p in front of you, then put a mirror on the floor (so that it's still at right angles to both you and the letter, but not upright). Now look at the image. This time it's a 'b'!
This works whether the mirror is on the floor or on the ceiling.
Reason: the image has been rotated around the horizontal axis - i.e. the axis the mirror has been placed in (the mirror is parallel to the floor). So you get the perception of 'upside-down' reversal.
One final aside: Look at yourself in a ceiling mirror. You won't be asking "why do mirrors reflect sideways but not upside down?". You'll be asking "why don't those people fall off the ceiling?"
And the moral of the story ...? Be clear what question you're really trying to answer (e.g. whether you're talking about an upright mirror or not).
(Boy, I'm gooood, aren't I! [^])
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I've been thinking about this more. (I'm sorry, it's becoming a bit of an obsession. Am I boring you yet? [:I]) Anyway, I've had a couple more thoughts.
Thought 1:
Maybe a better explanation than my previous posting is this:
Imagine a large hemispherical dome - say, 4m in diameter, 2m high - which is completely mirrored (silvered) on the inside.
Sit on the floor in the centre of this dome, with a large cardboard cutout of the letter 'p' standing upright on the floor directly in front of you (say, 1.5m from you).
Look in the mirror directly behind the letter. It still looks like a p. But as you move your eyes around the dome to the right (or left), the reflected image appears to rotate around a vertical axis, until it becomes flat (a side view), then continue and the image folds out into a 'q'.
But if you moved your eyes upward, it would rotate around a horizontal axis, so eventually flipping over into a 'b'.
And if you move your eyes around in random directions, the image would rotate simultaneously in both directions.
So proving that mirror images don't just change left-right, it depends on positions and angles.
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Thought 2:
Maybe the above only works because you're using a two-dimensional letter.
Try it with a right-handed corkscrew instead of a letter. (Or just use your right hand with thumb sticking up and fingers curled into a fist - you know, the rule you use to tell you which way a magnetic field goes around an electric wire, etc.)
The reflected image you see will be a left-handed corkscrew. And the image will stay a left-handed corkscrew no matter how you move your eyes around the dome. It may become upside down, but it will stay left-handed.
So therefore "chirality" (a posh word I've learnt for left/right-handedness[:)]) appears to be reversed in ANY reflection.
Which suggests an interesting idea (OK, dull to normal people, but interesting to me):
Imagine an electric circuit where you can tell at a glance which direction the current is flowing in (e.g. because of the +/- signs on the battery). Take a photo of it. Then take a photo of it's reflection in a mirror. Nobody will be able to tell which photo is the real thing and which is the reflected image.
But now place a compass at right angles to the electric wire and take the same two photos. Now you WILL be able to tell which picture is the reflection - it won't obey the right-hand rule any more (regarding the direction of flow of the magnetic current in relation to the electric current).
Interesting, no? (Oh alright then, it's about as dull as you can get, I know, I know. I'll shut up and go back to playing CounterStrike. Night all.)
[:)]
P.S. Just out of curiosity ... can anyone (anyone who's still awake, that is) tell me if my reasoning/prediction about a reflected electric circuit is correct?
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Yes that's a really fundamental bit of physical straight thinking
Learn, create, test and tell
evolution rules in all things
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quote:
2. Place the letter 'p' in front of you, then hold a mirror to your side (so that it's upright and at right angles to both you and the letter). Now look at the image of the letter in the mirror. You'll find it's no longer a 'p', instead it's a 'q'.
This works whether the mirror is on your left or on your right.
All I saw was the side of the letter.
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It was only a thought experiment, Eth.[:(]