viewnote12 - PHYS 302 Unit 12 Viewing Notes – Athabasca...

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Unformatted text preview: PHYS 302: Unit 12 Viewing Notes – Athabasca University PHYS 302: Vibrations and Waves – Unit 12 Viewing Notes Early in the lecture, Dr. Lewin refers to Isaac Newton’s (1643-1727) espousal of the particle view of light and its refutation by Thomas Young (1773-1829) in 1803. While Newton started presenting his results in the 1670s, Newton and Young’s work was presented together in the important book Opticks only in 1704 (now viewable at Google books). Christian Huygens (1629-1695) was roughly the contemporary of Newton. He formulated his wave theory of light before Newton’s particle view. Newton’s particle view of light explained reflection simply. It also explained refraction, with many elaborations. Newton’s influence, based on the scope of his experimental work (as outlined in Opticks), prevailed for nearly 100 years. We now know (as shown in earlier units with discussion of quantum mechanics) that not only does wave-particle duality apply to light, but also to particles. While a naïve view of the world is based on particles (allowing for successful analysis at the introductory level), in some sense particles do not exist, except as an abstraction or limiting case! A somewhat discouraging discussion about Huygens’ principle (also known as the Huygens-Fresnel principle in recognition of Fresnel’s work in building a theoretical framework after Young’s experiment) ends at 5:30. While Dr. Lewin describes the principle as “giving the right answer for the wrong reason,” in fact, Huygens’principle relates to the most advanced form of quantum mechanics: quantum electrodynamics (QED). In this approach, usually associated with Nobel Prize Winner (1965) Richard Feynmann, wavefunctions of an object propagate over any and all allowed (unobstructed) paths from the source of a target point. The result of interference (addition) of contributions from all paths defines the amplitude and phase of the wavefunction of the object at the measuring point, and it defines the probability of finding the object at this point. All particles have wave characteristics—not only photons, but also electrons, neutrons, protons, atoms, molecules, and in fact, all other objects. So, this “path integral” approach is, in principle, applicable to all particles. While applying the path integral approach may be difficult, Huygens’ principle allows simple visualization of a similar behaviour. Thus, it does have a physical basis, although Huygens could not have imagined this. Destructive interference, or light+light=darkness, results when a phase difference is ½ λ (6:50). Destructive interference takes place on hyperboloidal surfaces (as some geometry would show). Constructive interference may be less surprising than destructive interference, since it results in light+light=more light (however, as we will see below, more than one might initially expect). Constructive interference takes place when there is no phase difference. In both destructive and constructive interference, phase differences are cyclical: the angle goes through the 2π radians that constitute a full circle. The same behaviour results as one adds (through path length changes) integral multiples of 2π as phase differences (8:30). At a great enough distance, hyperboloidal surfaces appear to be nearly straight. As such, simplified analysis can proceed on that basis. If one is far away from two slits that are separated by a distance d and off the axis (perpendicular to the surface having the slits in it) by an angle θ, the difference in distance from the observation point to the slits is dsinθ (10:30). This is the physical path difference. As d a fraction of a wavelength this is sin . Since one wavelength corresponds to a 2π advance in phase, the increase in phase by this fractional increase in number of wavelengths (in the path) is d 2 sin . (Note that δ is pronounced delta and is the lower case form of Δ.) For constructive interference, where crests of waves add to crests of other waves to make a higher amplitude wave, one must have δ=n2π, where n=0,±1,±2,… (11:40). Another way to write this condition is dsinθn =nλ. For destructive interference δ=(2n-1)π or d sin n 2 n 1 (13:30). Next, 2 Dr. Lewin demonstrates red laser light (coherent light; see Reading Notes) of wavelength 600 nm going through two slits separated by 0.25 mm (¼ mm), viewed 5 m away. The constructive interference formula with λ=600 nm, L=5 m, and d=0.25 mm gives x±1=1.2 cm and x±10=12 cm (19:00). Dr. Lewin draws a sketch with maxima spaced in units of sinθ by λ/d. Note that for smaller wavelength light, the maxima will be spaced by less than λ/d (23:00). The sketch shown is for intensity, in units of W/m2. Now the shape of the curve as cos2 can be derived. With a phase difference of δ, the wave from slit 1 and slit 2 arrive as E1=E0cosωt and E2=E0cos(ωt-δ) and sum, using the familiar “cos half the sum times cos half the difference” identity, to Etot 2 E0 cos t cos (24:30). The 2 2 intensity is the square of the amplitude (the term Poynting vector is not explained in this course), so a cos 2 2 intensity results, with the first term having very rapid variation (of order 1015 Hz), which averages away (25:00). 1 PHYS 302: Unit 12 Viewing Notes – Athabasca University The demonstration is followed by some discussion of the wave-particle and detectability properties of photons (29:25). A slide shows the effects of wavelength. Sound interference occurs with all the same equations as for the case of light discussed above, but the wavelength of sound is much longer than that of light (in this case, 11.3 cm for 3000 Hz, with separation 1.5 m). As such, the sound in the video lecture demonstration should have 26 surfaces of interference (both minima and maxima) in the classroom. At a distance of 5 m, the angle of 4.3º from maximum to maximum corresponds to 38 cm. Dr. Lewin demonstrates sound interference before the break (38:20). So far, path difference has been obtained through simple geometry. Now we examine a slightly more complex way of getting path difference, through transmission and reflection in a medium. Consider a thin, horizontal oil film of thickness d between levels A and B, with index of refraction in the film of 1.5 (that of air is 1.0, above and below) (41:15). The index of refraction is the inverse ratio of the speed of light in vacuum and in the medium. That is, light travels 1.5 times slower in oil than in vacuum or in air. The reflection coefficients are the same as those for a paired rope with different speeds on either side of the joint, and the sign of reflection is negative (42:00). As you view the remainder of the video lecture, note that you will not be responsible for the mathematical explanations given. You are expected to know the following about thin films: 1) 2) 3) 4) Path differences can occur through combinations of reflection and phase changes at boundaries. Path differences give rise to phase differences that can cause destructive or constructive interference. Phase differences depend on the index of refraction of the medium, its thickness, and its wavelength. For some wavelengths, constructive interference can give rise to colours in thin films; for other wavelengths (e.g., long ones), this may not be possible. Anti-reflective coatings for light or other electromagnetic radiation can be made from appropriate thin films. This point is not covered in the lecture, yet is of great importance where reflections are not desired (e.g., eyeglasses) or where they are desired (e.g., heat-retentive windows). Also, the ideas presented that focus on optical wavelengths apply completely to other EM wavelengths. For example, a common cause of poor radio reception is “multipath,” in which waves that have reflected from various objects (e.g., buildings) recombine (having followed different paths) and cancel. This effect is not restricted to EM radiation, and is an important part of the acoustic design of buildings. 2 ...
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