![]() ![]() So this first null occurs when that happens. ![]() To be precise, if we draw a line from each oscillator to a distant point and the difference Δ in the two distances is λ / 2, half an oscillation, then they will be out of phase. We get the first minimum at a small angle away (the angle from the normal is denoted by ϕ in the illustration), where the arrival times differ by 180°, and so there is destructive interference and the intensity is zero. Indeed, the waves are perfectly in sync and, hence, add up, and the factor four is explained by the fact that the intensity, or the energy of the wave, is proportional to the square of the amplitude: 2 2 = 4. Once again, the waves emitted by the two point sources will be in phase in the east-west (E-W) direction, and so we get a strong intensity there: four times more, in fact, than what we would get if we’d just have one point source. ![]() In fact, the array consists of just two sources of radiation, separated by 10 wavelengths. In the set-up below, for example, we have an array of oscillators producing not just one but many maxima. Interference patterns can be complicated. That’s because the distance between the array and the point where we are measuring the intensity of the emitted radiation does result in a phase difference, even if the oscillators themselves have no intrinsic phase difference. We assume α is zero here, so the array produces a maximum in the direction θ out = 0, i.e. λ is the wavelength of the radiation that is being emitted, and α is the so-called intrinsic relative phase–or, to put it simply, the phase difference. radio waves, but it can also be higher-energy light) in an array of length L. We have eight point sources of electromagnetic radiation here (e.g. ![]() Let’s start with the right-hand illustration, which illustrates interference, not diffraction. Let’s have a look at it: light going through a slit or circular aperture, illustrated in the left-hand image below, creates a diffraction pattern, which resembles the interference pattern created by an array of oscillators, as shown in the right-hand image. To be fair, Feynman does use the phenomenon of diffraction to illustrate the Uncertainty Principle, both in his Lectures as well as in that little marvel, QED: The Strange Theory of Light of Matter–a must-read for anyone who wants to understand the (probability) wave function concept without any reference to complex numbers or what have you. Frankly, I think it does not get enough attention in textbooks, including Feynman’s, so that’s why I am devoting a rather long post to it here. Indeed, the phenomenon of diffraction–light, or an electron beam, interfering with itself as it goes through one slit only–is equally fascinating. And he could also have elaborated the phenomenon of electron diffraction. While it obviously illustrates “the basic peculiarities of quantum mechanics” very well, I think the dual behavior of light – as a wave and as a stream of photons – is at least as good as an illustration. It shows interference–a property of waves–of ‘particles’, electrons: they no longer behave as particles in this experiment. In his Lectures, Feynman advances the double-slit experiment with electrons as the textbook example explaining the “mystery” of quantum mechanics. If anything, the lack of illustrations will help you think things through for yourself. It should be possible, however, to follow the main story line. Pre-script (dated 26 June 2020): This post got mutilated by the removal of material by the dark force. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |