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

**Bernard Murphy, PhD, Chief Technology Officer, Atrenta Inc.**

12/1/2014 05:45 PM EST

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The more one looks into it, the more one realizes that aspects of mirrors that initially appear to be intuitive are, in fact, extremely hard to explain.

EE Times editor Max Maxfield recently offered this challenge in a comment on a previous post: "I still cannot wrap my brain around how mirrors work -- from simple things like why is the angle of incidence equal to the angle of reflection, all the way up to how the photons 'bounce' off the atoms forming the mirror without being scattered to the four winds, as it were."

He's not looking for an easy answer using basic optics or even Maxwell's equations. His question is based on Richard P. Feynman's 1990 book *QED: The Strange Theory of Light and Matter* (where QED stands for Quantum Electrodynamics). I thought that I would knock out a quick response with a few examples, but this has turned into one of the harder questions I have attempted. Getting to a reasonable answer has made me reset my own understanding.

In fairness to anyone who hasn't read the book, here is a highly condensed summary of how Feynman explains reflection. The idea is to sum components of reflection over all conceivable paths. We want to prove that the angle of incidence is equal to the angle of reflection (AOI=AOR), but we can't start with that assumption. Instead, we have to consider all paths. Feynman does this considering the experiment below -- looking at the various possible paths from the source reflecting off each part of the mirror and ending at the detector.

We sum contributions at the detector by considering each contribution as an amplitude with an associated phase (shown by the arrows below the mirror). We assume the only difference in phase between the paths is due to the lengths of the paths (more on this later), which results in phase shifts between contributions at the detector. The phase shift changes slowly around the center line (at which point AOI=AOR), where the path length varies slowly. The path length (and therefore the phase) changes faster as we move away from the center. When we add these contributions together, they add constructively near the center but increasingly cancel through phase mismatch as we move away from that center. As a result, we obtain a peak around AOI=AOR and very little intensity as we move away from the peak on either side.

All of this is understandable, but what does it have to do with QED? In researching this blog, I first thought Feynman was using creative license to keep his explanation simple. Then I decided he was bending the truth just a bit. Finally, I realized his explanation -- apart from minor details -- is completely accurate and is the most intuitive explanation of QED I can imagine. Thus, the best I can hope for is to add some color to that explanation.

Let's start by saying that we believe photons are real, because we can reduce light intensity until we see single flashes at the detector, and the flashes always have the same intensity for a given frequency of light. So light is quantized, but whatever behavior we invent for this new model, it must still correspond at a macro scale with everything we expect about light behaving as a wave. We also need to double-check what has to be new and what is really just unexpected classical behavior.

An apparent problem emerges in imagining the experiment being performed using a laser as illustrated below.

The light isn't going all over the place, so what gives? In fact, this experiment is a little deceptive. If we look at the mirror from behind the laser, we can see a light spot, which means that light is reflected back toward the laser. This means that, even at the macro level and even for a laser, light is scattered in all directions at reflection. On this point, Feynman's explanation is completely classical, though not the way we normally think about light. Scattering in this way also corresponds with Huygens' principle (1678) that a light wavefront advances by treating each point on the wavefront as a new wavefront, which expands in all directions.

Given this, summing up the paths accounting for phase is also completely classical. That's what you do with waves. There are just two problems. The first is how all this applies to photon "particles"; the second concerns the assumption about phase differences. On the first point, my reading shows two lines of thinking. The most heavily represented is what I'll call the "mystery and imagination" track. Quantum behavior is weird, and we can't really understand what is happening, but the math works. In the meantime, we wrestle with how to imagine a photon particle behaving like a wave. I think most of us are secretly attracted to this track, because it gives us exotic behaviors as fuel for philosophizing about exotic possible causes. Perhaps photons are extended wave packets and behave as waves. Perhaps the universe splits into multiple universes at each event such as reflection, and so on.

Rookie

McChalium_II 7/7/2015 2:56:13 PM

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Terry.Bollinger 12/3/2014 11:10:02 PM

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.

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GSKrasle 12/3/2014 8:13:58 PM

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mike_coln 12/3/2014 6:14:16 PM

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Terry.Bollinger 12/3/2014 1:41:00 PM

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, andunchangedfrom 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

continuoustransition 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

allforms 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!)Author

GSKrasle 12/3/2014 12:24:25 PM

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.

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traneus 12/3/2014 10:58:57 AM

"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.

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Max The Magnificent 12/3/2014 10:03:00 AM

anyone interested can look up this short essay onYour 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 momen

t.Author

Terry.Bollinger 12/2/2014 7:41:28 PM

In terms of

QED, however, thatiswhat 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

doend 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,allforms 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 onYour Quantum Mechanical Eye.Author

GSKrasle 12/2/2014 6:52:07 PM