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Magic Mirror on the Wall, How Do You Even Work at All?

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Keith Sabine
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The magic of mirrors
Keith Sabine   12/2/2014 10:11:52 AM
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Another oddity about mirrors is apparent if you stand in front of them. Raise your left arm. The image in the mirror raises its right arm. So horizontally, mirrors transpose left and right. But nod your head, and the mirror nods back without transposing up and down.

Max The Magnificent
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Re: The magic of mirrors
Max The Magnificent   12/2/2014 11:09:04 AM
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@Keith: Another oddity about mirrors is apparent if...

This is because we have two eyes separated horizontally -- also the way in which the brain's right hemisphere processes info from th eleft eye and vice versa -- if we had one eye located in the center of our forehead and the other on our chin and so forth, then the transposition effect woudl be in the vertical plane instead of the horizontal.

Keith Sabine
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Re: The magic of mirrors
Keith Sabine   12/2/2014 11:36:07 AM
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Indeed Max, we are horizontally symmetrical but not vertically symmetrical... but it's our brain which is doing the processing of what is left and what is right. And our brain is conditioned to thinking (for millions of years) that the mirror is not really there, so it inverts right and left.

RichQ
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Re: The magic of mirrors
RichQ   12/2/2014 12:33:58 PM
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It seems to me that the problem is our use of the terms "left" and "right" which are relative to the observer. If we are facing east, looking at ourselves in a mirror that is "facing" west, the hand on the north is the same for both the person and the image. There is no reversal occurring in the plane of the mirror. As you say, our brains insist on perceiving the reflection as though it were an object and assigning left and right attributes based on that mental model, then mentally rotating the model about the vertical axis to form the model for the object facing us. It's the mental rotation that reverses the right and left-handedness of things. But the reflection isn't a rotation, it's a reversal in the direction normal to the plane of the mirror, and that is different. The world we percieve in the mirror has a coordinate system that is left-handed where ours is right-handed, because only the z-axis (the one into the mirror) has been reversed. X and Y in the plane of the mirror are not reversed.

Another way of thinking about it is that the object in the mirror has been reversed in the z-axis only. If it were a physical transformation, it would be like having every atom in our body reverse its front-to-back position. Left and right, top and bottom remain the same. But if we were to do that in real life, what we called our right hand would now be our left.

By the way, if you want a reflected image that looks like you facing yourself, put two mirrors together at right angles to one another and look at the reflection occurring at the seam. It is the result of a double reflection from you to one mirror then to the other mirror before returning to you. That does reverse right and left, but not top and bottom because that is the axis of symmetry for the reflection. The image you see will look like your clone looking back at you (except for the seam line).

 

DougInRB
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Re: The magic of mirrors
DougInRB   12/2/2014 12:40:21 PM
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@RichQ: Great (and simple) explanation.  Thank you!  I feel better now.

Max The Magnificent
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Re: The magic of mirrors
Max The Magnificent   12/2/2014 2:06:48 PM
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@RicjQ" It seems to me that the problem is our use of the terms "left" and "right" which are relative to the observer.

You'd prefer "Port" and "Starboard"?

RichQ
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Re: The magic of mirrors
RichQ   12/2/2014 2:22:40 PM
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I'd perfer port and brandy.

Max The Magnificent
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Re: The magic of mirrors
Max The Magnificent   12/2/2014 2:24:33 PM
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@RichQ: I'd prefer port and brandy.

I'll drink to that! LOL

anon0735652
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Re: The magic of mirrors
anon0735652   12/2/2014 12:08:20 PM
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We see our left side on the left side of the mirror, our hair at the top, etc. The 'transposition' is simply us trying to turn ourselves around in our mind to imagine what we look like based on the image in the mirror. We could just as easily imagine ourselves upside-down instead but that is not the way our minds work since our pre-processing based on evolutionary usefulness with most external arrangement and movement occuring in the horizontal plane (that also being the reason why our eyes are horizontally spaced, i.e. the eye arrangement is a result of the same cause but is not the cause).

Regarding the core question about the paths, it seems that the discussion falls into the common trap of asserting the particle-wave duality while dwelling on the discrepancies that arise when considering the photon as one or the other or both in a conventional sense, which it is not! Just think about the definition of 'path'. What are those lines that were drawn? What is moving along them? The answer is that nothing is moving along those paths specifically. The photon is only localized at emission and detection. However, those paths can be considered as building blocks to the complete 'path' in a similar fashion to how a line segment is an approximation of part of a curve.

DougInRB
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Re: The magic of mirrors
DougInRB   12/2/2014 12:36:51 PM
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Hang on a minute.  If we blame our brain on the transposition, why does it still look transposed when we take a photo of a mirror image and look at the photo later?  This is especially obvious when there are letters being reflected.

This all seemed so simple before I read this article.  Why did you have to mess with my brain???

 

Max The Magnificent
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Re: The magic of mirrors
Max The Magnificent   12/2/2014 2:05:33 PM
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@DouglnRB: This all seemed so simple before I read this article.  Why did you have to mess with my brain???

It's just one more service we offer (along with Zapping Things with ESD)

Duane Benson
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Re: The magic of mirrors
Duane Benson   12/2/2014 1:19:51 PM
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The mirror image isn't really reversed. When you look into a mirror, you're  essentially standing behind yourself and looking at your back side.

Except that you've removed your back skin and everything up to such a thin layer of your front side that it has all of the color and shape of your actual front side. You're looking at your back side with the imagery from your front side layered on top. So, when you move your right arm, the mirror image is also moving its right arm.

Or something like that

mike_coln
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Re: The magic of mirrors
mike_coln   12/3/2014 6:14:16 PM
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I would say that mirrors do not transpose either left versus right, nor top versus bottom. Instead they transpose front versus back. Consider the image you would see if the mirror was not there, and you were behind it.

Terry.Bollinger
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Re: The magic of mirrors
Terry.Bollinger   12/3/2014 11:10:02 PM
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You are exactly correct that the real transformation is front-to-back. That is, if the plane of a vertical mirror is labeled X (horizontal) and Y (vertical) and the axis perpendicular to it Z, then the virtual image formed by the mirror is actually invariant in X and Y, but translated (moved to the other side of the mirror) and inverted (reversed front-to-back) in Z.

To achieve this transformation physically, you would have to take a very thin rubber mold of, for example, your own face. The mask would need to transfer colors and textures to both sides. Once made, you would next need to flip the mold inside out and force yourself to imagine the now-convex inside surface of the mask as the outer surface of a real face. Our brains don't readily accept that severe of a transformation to a solid face, unless maybe you are Hannibal Lecter, so they instead try more "reasonable" transformations such as left-to-right or up-to-down. The visual outcome is similar, at least if you don't worry about the lack of solidity behind the image.

McChalium_II
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Re: The magic of mirrors
McChalium_II   7/7/2015 2:56:13 PM
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Does this mean that those arrays of mirrors that create the so-called infinity effect are actually windows into myriads of alternate universes? Maybe I should go read Feynmans book. If it is as good as his "Surely you Jest" book it'll be a good read even if I don't understand a word of it.

Max The Magnificent
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Still Confused
Max The Magnificent   12/2/2014 11:26:34 AM
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Hi Bernard -- thanks for this explanation, but I'm still confused.

As I mentioned before, I've read Richard Feynman's book QED: The Strange Theory of Light and Matter, and I follow the idea that the photons can (and do) take every possible path (even though this makes my mind throw a bit of a wobbly); also that phase changes between the various paths result in a peak such that the angle of incidence = the angle of reflection.

I've also read The Quantum Universe: (And Why Anything That Can Happen, Does) by Brian Cox and Jeff Forshaw, which covers the same thing is a slightly different way.

But even accepting all of this -- the surface of the mirror is composed of atoms -- and although it looks smooth at our macroscopic level, when we "zoom in" it would look like the surface of the moon at the atomic/photonic level with all sorts of "bumps" and suchlike, which you would think would scatter the light in all directions.

And then we have the fact that the electron shells surrounding an atom aren;t spherical -- they come in all sorts of weird and wonderful shapes (yes, I know they aren't hard shells -- rather probabilities and stuff).

And then we have the fact that -- as far as I understand it -- a photon doesn't "bounce" off the electron shell an atom like one billiard ball bouncing off another -- instead it raises an electron to a higher energy level -- then at some time in the future that electron falls back to its original energy level and emits a new photon -- but what's to say that this photon won't head off in any direction...

My noggin hurts...

Duane Benson
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Re: Still Confused
Duane Benson   12/2/2014 1:25:05 PM
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'the surface of the mirror is composed of atoms -- and although it looks smooth at our macroscopic level, when we "zoom in" it would look like the surface of the moon at the atomic/photonic level with all sorts of "bumps" and suchlike, which you would think would scatter the light in all directions.'

Given that there is so much space between the electrons and the nucleus, zoom in enough and rather than a bumpy surface, it would look more like empty space. Light should simply pass through all of that space and we shouldn't be able to see anything at all.

ccorbj
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Re: Still Confused
ccorbj   12/2/2014 1:35:38 PM
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@Max - ah, I see. I took at shot at the point of confusion, but obviously missed the mark. I have a follow-up blog which talks about the wavelike nature of photons (and particles) being more fundamental than their particle nature, so to some extent, the idea that a photon is a little bullet may be part of the confusion. Even though quantized, a photon is a difficult thing to localize thanks to Heisenberg, indistinguishability and travelling at the speed of light. In a semi-classical sense, it is still a fairly extended wave reflecting off the mirror. It just happens to have a fixed amount of energy.

Making this more confusing, a photon even though poorly localized can be absorbed as a unit into an atom, bumping an electron to a higher shell, or out of the atom. But that isn't necessarily what happens when an electron hits a mirror. A mirror is a solid (usually), so the photon is interacting with solid behavior - bands and phonons  and so on. The current state of understanding of reflection is that the photon isn't exactly absorbed and re-emitted. Instead it couples with an internal excitation in the solid (an exciton) to form something called a polariton-exciton. This travels at the surface of the interface (between glass and air, or between metal and glass) until the photon is released. No particular reason it should be released in any particular direction, at least as far as I have found, so you just assume it randomly heads off in whatever direction. But there is a mystery in this that I have not been able to figure out. Why do you get a 180 degree phase shift independent of how long that excitation lived, or direction of release? Without a fixed phase shift, Feynman's argument wouldn't work.

All of which probably makes the whole topic even more wobbly. But madness awaits if you are hoping for sanity in quantum anything.

GSKrasle
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Re: Still Confused
GSKrasle   12/2/2014 3:34:22 PM
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Max,

 

It gets worser! 

Back in my MatSci/Metallurgy days, I did a big research project on why metals are, well, metallic. In particular, why Cu and Au are coloured, and the chemically/electronically very similar Ag is not. 

There are a lot of presumably equivalent models that apply to light/EM reflection (and transmission), some particularly applicable to metals, some to anything metallic-looking, and some that are more general. Modeling metals as a conductive 'gas' of electrons with a periodic (or for liquids, a statistically-distributed) lattice of positive charges works, and gives a 'plasma temperature' for the 'gas' which is very high and an amusing thing to contemplate. Impinging EM fields induce currents, which can (depending on the local resistance, inductance, capacitance [which are affected by the relativistically-adjusted electron{/hole} mass and the positive lattice]), produce a new outgoing EM field with, you guessed it, the characteristics we expect in a metallic reflection. But that model is inapplicable to non-metals, where reflections also have a peculiar dependency on the polarization of the incident EM field. But for metals, this model makes light reflection similar to antenna reflection. Modeling the surface as a mismatch in the complex electromagnetic impedance works too (and was the most successful for my purposes). (The complex refractive index is a function of λ, ε, μ, and all sorts of other parameters.)

Long story short, Ag IS coloured... if you're an insect. Cu, Ag and Au basically have a low-pass in their reflection characteristics, as does everything, but Cu is in the green, Au in the blue, and Ag in the near-UV. On a larger-scale than the narrow window of human visual sensitivity, they look very very similar. Li also has interesting characteristics, and both the colours of the transmitted light (if you have a thin enough layer) and of the liquid metals are interesting. A practical consequence is that UV and a UV-sensitive camera can be used to distinguish Ag- from Al-plated chips (which was once important to me when some dice got mixed and had to be non-contaminatedly segregated).

Oh, and your concern about 'bumpiness' of the surface applies only if that 'bumpiness' is comparable-to or larger than the incident wavelength (and THAT may depend on incident angle)....

Which brings me to my image-processing/software days: When rendering an image, the brightness of the light from a point on a surface varies according to how close (angularly) the eye is to the perfect specular direction. For matte objects, that specular reflection brightness may be modeled as proportional to (cos(θ)), where θ is the angle from the viewing direction to the ideal specular direction. For shinier objects, there is an exponent: (cos(θ))^n, with n=>∞ for metallic reflection. (Phong Shading in Raytracing). So 'reflections' from your bumpy surfaces will actually have an exponent n which is a function of λ, just as the components of the complex index of refraction (n, κ) are.

And then it starts to get complicated and confusing; I doubt this site would be happy if I dumped a bunch of equations on it.... 

Max The Magnificent
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Re: Still Confused
Max The Magnificent   12/2/2014 3:47:20 PM
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@GSKrasle: ...and then it starts to get complicated and confusing...

I'm laughing through my tears :-)

ccorbj
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Re: Still Confused
ccorbj   12/2/2014 4:58:54 PM
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@GSKrasle - love it! Welcome to our mutual descent into madness. One of the things a photon can couple to is a plasmon, an excitation in the electron gas in a metal. Thanks for the added detail. All this goes to shows, the deeper you dig, the more confused you are going to get.

And then there's the measurement problem, which is only for advanced insanity...

GSKrasle
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Re: Still Confused
GSKrasle   12/2/2014 6:52:07 PM
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ccorb: Madness indeed. My advisor, who was in a position to understand the answer (or how to get it) to Ag colour, repeatedly told me 'you don't really want to know at the cost it would take to find-out' or something to that effect. I found-out, and now, if someone asks me to explain, you can guess how I reply.

Terry.Bollinger
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Re: Still Confused
Terry.Bollinger   12/2/2014 7:41:28 PM
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Max, you raised an interesting point earlier about how photons can reflect smoothly from a room temperature mirror. After all, at the atomic level the mirror surface should look like a chaotic jungle of wildly vibrating atoms and molecules, a chaotically kinetic kluge that should kick any particle-like photon off in a completely random direction.

In terms of QED, however, that is what happens. Feynman just doesn't get into that level of detail in that short, intentionally non-mathematical book.

That is, all of those "not really there" photons in the path integral really do end up bouncing randomly from all of those thermal atoms. However, since the total amplitude added by each such impact is proportional to the amount of turf occupied by the atom, the individual reflections are very weak. And while you might expect so many reflections to add up to a powerful overall effect, the fact that they are both random and complex (vs real) values means they tend very strongly to cancel each other. Only those components of the reflections that are in phase, e.g. due to long-range order (smoothness) in the mirror, will ever add up into a "signal" (amplitude, square root of the probability) that makes it likely the photon will travel in that direction. A fairly accurate classical analogy would be an ocean wave reflecting from a rough stone wall, with the wavelets bouncing from individual grains of the wall corresponding to the atomic-scale, non-reinforcing reflections of the mirror.

The answer I like best, however, is that neither reflection nor refraction are really classical phenomena. That is, all forms of smooth, optically coherent light bending are profoundly quantum mechanical in nature, even when their outcomes can be expressed in simple equations. That's way too much to get into here, but anyone interested can look up this short essay on Your Quantum Mechanical Eye.


Max The Magnificent
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Re: Still Confused
Max The Magnificent   12/3/2014 10:03:00 AM
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@Terry: ...anyone interested can look up this short essay on Your Quantum Mechanical Eye.

Hi Terry -- thanks for this -- I just took a quick look -- I'll be returning to peruse and ponder your essay in more depth as soon as I get a free moment.

Some Guy
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Inquiring minds ...
Some Guy   12/2/2014 4:36:53 PM
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... just want to know:

Why does a mirror swap left and right,

but not up and down?

 

even after you rotate it from portrait to landscape?

mhrackin
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Re: Inquiring minds ...
mhrackin   12/2/2014 5:22:54 PM
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@some guy: The answer was already given in an earlier post: it's basically all in your head! Try it lying down....

Some Guy
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Re: Inquiring minds ...
Some Guy   12/2/2014 6:18:56 PM
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@mhrakin

"... all in your head!"

I've suspected this for some time now. And my kids will tell you they knew it all along.

Max The Magnificent
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Re: Inquiring minds ...
Max The Magnificent   12/2/2014 6:32:02 PM
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@some guy: ...even after you rotate it from portrait to landscape?

ROFLOL

traneus
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Re: Inquiring minds ...
traneus   12/3/2014 10:58:57 AM
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@SomeGuy:

"Why does a mirror swap left and right but not up and down?"

A mirror swaps front and back.

The front (closest to the mirror) part of the object is the front (closest to the mirror) part of the reflected image. The back (farthest from the mirror) part of the object is the back (farthest from the mirror) part of the reflected image.

The left and right swap is our interpretation of the front and back swap. Due to gravity, we find rotating about our head to foot axis much more plausible than rotating about our left to right axis.

GSKrasle
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Re: Inquiring minds ...
GSKrasle   12/3/2014 12:24:25 PM
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traneus,

 

EXACTLY. 

As I touched on a couple of months ago (http://www.eetimes.com/messages.asp?piddl_msgthreadid=46313&piddl_msgid=322067#msg_322067):

because of our psychology and bilateral (near-) symmetry, we have a hard time understanding until we abstract the question into symbolic form. 

While not strictly "mirror"-related, the geometry of (chemistry) chirality is as hard to believe: if any two bonds of a chiral atom are exchanged, the result is the mirror-image of the original; exchanging another random two returns it to the original state.

Terry.Bollinger
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Re: Inquiring minds ...
Terry.Bollinger   12/3/2014 1:41:00 PM
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I tried to resist this very different topic offshoot, but I can't... :)

Using box-shaped room coordinates, stand near the back wall of a room that has some kind of text, say a poster, on the far wall in front of you.

Hold a flat mirror out to your left, keeping it parallel to the left wall of the room, and look at the poster image in the mirror. As you would expect, you will see the poster inverted left-to-right, and unchanged top-to-down. No big surprise there, right?

Now circle your arm upward in an arc until the flat mirror is instead parallel to the ceiling. Look at the image of the poster again. What do you see?

The same poster... only this time it is inverted up-to-down, and unchanged from left-to-right...

Uh, say what?

What's even more fun is that if you move your arm smoothly and keep the poster image centered within the mirror frame at all times, you can watch every step in the continuous transition between the "standard" left-to-right inversion and the unanticipated up-to-down inversion. Be sure to ask yourself when, exactly, the transformation takes place...  }8^)>

(Meanwhile, if you like quantum stuff, don't forget my earlier reply below about how all forms of reflection and refraction require quantum mechanical "scoping out" of the human-scale shapes of large objects. The quantum world is always watching you, quite literally!)

 

GSKrasle
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Re: Inquiring minds ...
GSKrasle   12/3/2014 8:13:58 PM
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Or for that matter, take a hand-lens and hold it close to your monitor. It magnifies, right? Now move it towards your eye; eventually you see an inverted image. (You may have to fuss with distances.) What's up with that?

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