标签: MIRROR

Max Maxfield recently offered this challenge: "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. I'll call the other track "mostly classical." As far as I can tell, it is represented solely by Feynman and a Geneva University theoretician who applied the Feynman path approach to detailed calculations of reflection, refraction, diffraction, and other phenomena in 2005. This paper is quite technical but still worth a read. Though all other authors acknowledge Feynman's genius, it seems that few if any actually use his methods in QED calculations, because they are typically more complex to apply than Schrodinger-based approaches .   The Geneva paper seems to be the first time anyone has documented detailed consequences of the Feynman model. (Feynman didn't record his own calculations for this example.) But before I go there, let's look quickly at the other problem: that phase assumption. Path length is certainly a factor in phase at detection, but what about the phase when a photon starts on one of these paths? If the source is a laser, you can assume phases are equal at creation, but this is not the case for a regular light source. If you assume that amplitude summing (interference) at the detector is between different photons travelling on different paths, path differences still affect the result, but lack of correlation between source phases will lead to random and time-varying (noisy) interference at the detector, which is not what we see.   Back to what the Geneva paper has to say: - Feynman's explanation is more fundamental and more powerful than the Schrodinger approach. Schrodinger can be derived from Feynman, but not vice versa , because Feynman represents correlation between space-time events (between paths), but Schrodinger cannot. - In detailed calculations using the Feynman method applied to photons, all classical behaviors of light as waves emerge as expected. Reflection, in particular, follows Feynman's example. - Photons propagate over macroscopic distances in a completely classical manner. (Heisenberg applies to the creation and detection of a photon and to scattering events, but not to simple propagation.) But we must consider all possible paths in the analysis. - Paths add in the same way that waves add. We add amplitudes with phases to obtain interference at the point of detection. - This brings us to the creation phase issue and the only conceptually difficult requirement of the Feynman method. Different photons have random relative phases at creation, but any given photon is trivially in phase with itself when created. Therefore, to obtain the results we see, interference cannot be between different photons travelling different paths. Each photon individually must travel along all possible paths and (indelicately) interfere only with itself at detection. This is the only way we can avoid that noisy interference between uncorrelated photons, and it is why experiments testing one photon at a time give the same results as for multiple photons at the same time.   I should caution that the 2005 paper is an interpretation, and that it makes predictions of new behaviors that have not yet been tested. But absent counterexamples, I find this interpretation very appealing. It is in complete agreement with Feynman's explanation, and it conserves all classical and intuitive understanding of light behavior based on photons, with just one exception. That exception is a doozy: A photon must travel simultaneously along all possible paths to the point it is detected and resolve itself through self-interference at detection. If we suspend disbelief on this one point, everything else is completely intuitive.   So what do we make of this one difficult point? Travelling simultaneously along all possible paths is definitely neither classical nor intuitive. Perhaps we see a particle travelling along all paths as a projection from a simpler path in something more fundamental than space-time. There are hints of this in a recent article, " A jewel at the heart of quantum physics ," which suggests that the space-time so familiar to us may not be the most basic representation of reality. Whether we will appreciate this as an improvement in intuitive understanding is up for debate.   Bernard Murphy, PhD Chief Technology Officer Atrenta Inc.

As you may remember, a month or so ago I decided to create an infinity mirror . Of course, the infinity mirror concept isn't new, but I've never actually made one myself. It also gives me a chance to play with a 1-metre length of NeoPixel Strip I acquired from Adafruit.com .   NeoPixel strip from Adafruit (60 tri-colour LEDs per metre).   This stuff is pretty amazing. There are just three wires running down the length of the strip: power (+5 V), ground (0 V), and a signal line. Using this signal line (and therefore only one digital pin on your Arduino), you can individually control the colour and brightness of each pixel. You can also download a corresponding Arduino library and examples from the Adafruit website, which makes everything just about as easy as it could be. These NeoPixels are amazingly bright, to the extent that you can't really look at them head-on when they are at full intensity. I'm planning on using them for all sorts of projects, of which my infinity mirror is just one. The thing about infinity mirrors is that you can find all sorts of images and descriptions on the web, but most of them are rather vague when it comes to the nitty-gritty details. For example, they may tell you to use a full mirror on the back and a half (one-way) mirror on the front, but they don't even hint as to the optimal gap between the two mirrors. Similarly, you may find a how-to article saying that you can form your one-way mirror using a piece of regular glass covered with a sheet of the film they use to tint car windows, but they don't say what type of film to use (there are lots of different shades, including mirrored ones). Fortunately, "I R an Engineer" and I'm quite happy to experiment for myself. My first step was to determine the optimal gap between the two mirrors. I started by creating a crude prototype frame using four strips of wood with a 0.5" x 0.5" cross-section. I spray-painted these gloss black and placed them on top of the full mirror. I then used a couple of thin strips of painter's masking tape to temporarily attach one end of my NeoPixel strip to one of these pieces of wood, after which I laid the half mirror on top.       Test frame formed from a single 0.5" row. In this experiment I was only lighting 16 or so NeoPixels at the end of the strip. You can see the unlit pixels on the rest of the strip as it exits my mirror from the upper right-hand corner. The far end of the strip (not visible in this image) is connected to an Arduino Uno. Eventually, I will end up wrapping the entire strip around the inside of the frame, but that's still in the future. My next experiment was to leave the original four 0.5" strips and NeoPixels where they were, but to add a second 0.5" strip on top of the first. The result was for the reflections to come in pairs as shown below: Test frame formed from two 0.5" rows with the NeoPixel strip attached to the bottom row. Next, I swapped things over so that I started with a 0.5" strip without LEDs on the bottom and then added the strip with the NeoPixels on the top. This time we see a single row of lights at the top, followed by pairs of rows fading off into infinity as shown below:     Test frame formed from two 0.5" rows with the NeoPixel strip attached to the top row. Finally, I used three rows of 0.5" wooden strips, with blank rows at the bottom and top and the NeoPixel row in the middle. The result—as compared to the first test using only a single wooden strip—is to have a wider gap between the reflections and for the reflections to appear to go much deeper (further) as shown below:     Test frame formed from three 0.5" rows with the NeoPixel strip attached to the middle row. As we can see by comparing the above images, the advantages of having only a 0.5" gap between the back and front mirrors is that the resulting infinity mirror is really thin and it gives the impression you have many rows of LEDs mounted in close proximity to each other. The disadvantage is that the reflections fade away quite quickly. By comparison, the advantage of having a 1.5" gap between mirrors is that the reflections appear to continue longer (and deeper). The disadvantages are that the infinity mirror is thicker (chunkier) and the rows of reflections are spaced further apart. In the end I went for a compromise and decided to use a 1.25" gap between the mirrors. My chum Bob, who lives in the office next to mine, has access to all sorts of saws and tools in a warehouse just around the corner from this building. He just popped out and whipped up the pieces for the real frame as shown below:   The pieces for the real frame, which provides a 1.25" gap between the full and half mirrors. Sometime over the coming holiday weekend I will assemble the frame and mount the NeoPixel strip all around the inside. My next step will be to experiment with different types of automotive window-tinting film (my original experiments as shown above were conducted using a real one-way mirror). I shall, of course, report back as to the results of my experiments in a future blog. In the meantime, have you ever played with this infinity mirror concept yourself?  

车机逐渐冷落，但是冷落之中也有一些热点呈现，指望这些热点可以让自己的产品增加一些卖点，也是常情。只不过这些所谓的热点，各有各的尴尬之处。 OBD，语音控制，实时路况和Mirror Link 可以称上 车机的四大鸡血！   先说说Mirror Link 吧。笔者在2010年初上海工作时，就已经提出这个概念。当时所在公司为荣威350车子配套推出了一个采用Marvell PXA310 CPU和安卓1.5 版本的一个3G 安卓车机终端。基于这个汽车智能终端发展的思路，本人规划了一个产品，就是采用简化设计的车机终端。当做Monitor ，连接手机以实现手机的功能。这么想的原因，是因为车机的智能化难度比较高，而2010年正值各类智能手机的爆发式增长。   但是此计划终于搁浅并最终放弃。原因是，做不到我对Mirror Link 定下的三项基本原则：   1、双向操控 2、无延时 3、不能采用定制手机。   显然，这三条在当时的技术环境下是无法同时满足的。

Welcome to this week's blog in which we pause for a moment to take a deep breath (hold it... hold it... now exhale), slow down, relax, and start winding down in preparation for the weekend. As part of this exercise, I've gathered a few choice diversions for your delectation and delight. This week's humble offerings are as follows: No. 1: We're going to start with what I think is the best "feel good" video of all time. Even if you've seen this 100 times, it's still worth another look. And if you haven't seen it yet, then you are in for a real treat. It involves a young lad called Matt Harding who toured the world performing a silly little jig in each country he visited. The result—backed by the most amazing soundtrack—is nothing short of uplifting; you simply cannot watch this without thinking happy thoughts and realising that the world is truly a wonderful place. Click here to feast your eyes. Make sure your computer's sound is turned on. No. 2: Next we have one of the best pranks I've ever seen. Imagine you are leaving the office on your way home from work when you suddenly hear screaming and... All I can say is that I so want one of these dinosaur costumes! Click here to laugh out loud. No. 3: Speaking of pranks, here is a very technical one that makes it look as if the floor is falling away from under the people in a lift. I cannot imagine what I would think if this had happened to me. Click here to see more. No. 4: Arrggh... Now I've got pranks on the brain. The previous prank was highly technical, but you can create the illusion of reality in many ways. I am, of course, thinking of the classic "Bathroom Mirror" prank. Click here to see "double trouble." No. 5: I have to say that I love watching these funny videos. And, speaking of funny videos, I was recently introduced to one of the funniest cat videos I've ever seen. It's in French (with subtitles), which, for some reason, just works incredibly well. Click here to enjoy a "purrfect" break. No. 6: Of course, as soon as someone says "cat video," I immediately think of the "Cowboys Herding Cats" video—the script is laugh-out-loud funny. Click here to be transported to a different time. I tell you, I could keep this up for hours. I have so many interesting websites and videos to share, but I don't want to tire you out, so just make sure to keep your eyes open for my next "Cool Beans" column. Meanwhile, which was your favourite item out of this week's offerings? And, if you know of any interesting sites you'd care to share, please share them in the comments section below.