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.
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