Any chance of getting diffracted tonight? Diffraction, its applications and limits“ At a beach in Tel Aviv, Israel, plane water waves pass through two openings in a breakwall. Notice the diffraction effect—the waves exit the openings with circular wave fronts, as in Figure 37.1b. Notice also how the beach has been shaped by the circular wave fronts. p.1178

At a beach in Tel Aviv, Israel, plane water waves pass through two openings in a breakwall. Notice the diffraction effect—the waves exit the openings with circular wave fronts, as in Figure 37.1b. Notice also how the beach has been shaped by the circular wave fronts. p.1178

Figure 37.3 An interference pattern involving water waves is produced by two vibrating sources at the water’s surface. The pattern is analogous to that observed in Young’s double-slit experiment. Note the regions of constructive (A) and destructive (B) interference. Fig 37-3, p.1179

Interference of waves Constructive Destructive Fig 37-3, p.1179 Figure 37.3 An interference pattern involving water waves is produced by two vibrating sources at the water’s surface. The pattern is analogous to that observed in Young’s double-slit experiment. Note the regions of constructive (A) and destructive (B) interference. Fig 37-3, p.1179

Figure 37.1 (a) If light waves did not spread out after passing through the slits, no interference would occur. Fig 37-1a, p.1178

Figure 37.1 (b) The light waves from the two slits overlap as they spread out, filling what we expect to be shadowed regions with light and producing interference fringes on a screen placed to the right of the slits. Fig 37-1b, p.1178

Figure 37.4 (a) Constructive interference occurs at point P when the waves combine (All figures not to scale.) Fig 37-4a, p.1179

Figure 37.4 (c) Destructive interference occurs at R when the two waves combine because the upper wave falls half a wavelength behind the lower wave. (All figures not to scale.) Fig 37-4c, p.1179

Figure 37. 4 (b) Constructive interference also occurs at point Q Figure 37.4 (b) Constructive interference also occurs at point Q. (All figures not to scale.) Fig 37-4b, p.1179

Active Figure 37.2 (a) Schematic diagram of Young’s double-slit experiment. Slits S1 and S2 behave as coherent sources of light waves that produce an interference pattern on the viewing screen (drawing not to scale). Fig 37-2a, p.1179

Figure 37.7 Light intensity versus d sin  for a double-slit interference pattern when the screen is far from the two slits (L >> d). Fig 37-7a, p.1184

Demo slits Demo slits + laser CD + laser Figure 37.7 Light intensity versus d sin  for a double-slit interference pattern when the screen is far from the two slits (L >> d).

Quantum Weirdness Figure 38.26 Crystalline structure of sodium chloride (NaCl). The blue spheres represent Cl- ions, and the red spheres represent Na+ ions. The length of the cube edge is a = 0.562 737 nm.

Will depend on wavelength = spectrometer Figure 37.4 (a) Constructive interference occurs at point P when the waves combine. (b) Constructive interference also occurs at point Q. (c) Destructive interference occurs at R when the two waves combine because the upper wave falls half a wavelength behind the lower wave. (All figures not to scale.) Fig 37-4, p.1179

Figure 37.5 (a) Geometric construction for describing Young’s double-slit experiment (not to scale). (b) When we assume that r 1 is parallel to r 2, the path difference between the two rays is r 2 r 1 d sin  . For this approximation to be valid, it is essential that L >> d. n l = d sin q Fig 37-5, p.1180

Figure 38. 20 (Conceptual Example 38 Figure 38.20 (Conceptual Example 38.6) A compact disc observed under white light. The colors observed in the reflected light and their intensities depend on the orientation of the disc relative to the eye and relative to the light source. Fig 38-20, p.1221

Demo slits Confinement of a wave Interference with the back-reflected wave = standing wave Only discrete solutions = Quantum Mechanics Figure 37.7 Light intensity versus d sin  for a double-slit interference pattern when the screen is far from the two slits (L >> d).

Active Figure 18. 10 (a) A string of length L fixed at both ends Active Figure 18.10  (a) A string of length L fixed at both ends. The normal modes of vibration form a harmonic series: (b) the fundamental, or first harmonic; (c) the second harmonic; (d) the third harmonic. At the Active Figures link at http://www.pse6.com, you can choose the mode number and see the corresponding standing wave. Fig. 18.10, p.553

Figure 41.7 Potential-energy diagram of a well of finite height U and length L. The total energy E of the system is less than U. Fig 41-7, p.1334

Active Figure 41. 8 (a) Wave functions y Active Figure 41.8 (a) Wave functions y. The wave functions and probability densities are plotted vertically from separate axes that are offset vertically for clarity. The positions of these axes on the potential-energy function suggest the relative energies of the states, but the positions are not shown to scale Fig 41-8a, p.1335

Figure 18.21 Representation of some of the normal modes possible in a circular membrane fixed at its perimeter. The pair of numbers above each pattern corresponds to the number of radial nodes and the number of circular nodes. Below each pattern is a factor by which the frequency of the mode is larger than that of the 01 mode. The frequencies of oscillation do not form a harmonic series because these factors are not integers. In each diagram, elements of the membrane on either side of a nodal line move in opposite directions, as indicated by the colors. (Adapted from T. D. Rossing, The Science of Sound, 2nd ed, Reading, Massachusetts, Addison-Wesley Publishing Co., 1990) Fig. 18.21, p.563

Fig 41-CO A quantum corral shows two aspects of current technological advances in physics. The first aspect involves control over individual atoms. This corral is formed by positioning iron atoms in a stadium-shaped ring on a copper surface. The second aspect is the ability to image the individual atoms with a scanning tunneling microscope. The corral can be used to study the quantized states of electrons trapped in a small region. (Courtesy of IBM Research, Almaden Research Center. Unauthorized use prohibited.) Fig 41-CO, p.1321

Figure 37.3 An interference pattern involving water waves is produced by two vibrating sources at the water’s surface. The pattern is analogous to that observed in Young’s double-slit experiment. Note the regions of constructive (A) and destructive (B) interference.

How good is a microscope? – The Diffraction Limit In order to resolve 2 closely spaced structures you need to capture at least the first diffraction max. n l = d sin q d = l / sinq Figure 38.26 Crystalline structure of sodium chloride (NaCl). The blue spheres represent Cl- ions, and the red spheres represent Na+ ions. The length of the cube edge is a = 0.562 737 nm.

Figure 37.3 An interference pattern involving water waves is produced by two vibrating sources at the water’s surface. The pattern is analogous to that observed in Young’s double-slit experiment. Note the regions of constructive (A) and destructive (B) interference.

Diffraction limit in making small things: Your computer chips Figure 38.26 Crystalline structure of sodium chloride (NaCl). The blue spheres represent Cl- ions, and the red spheres represent Na+ ions. The length of the cube edge is a = 0.562 737 nm.

Diffraction limit in making small things: Your computer chips Figure 38.26 Crystalline structure of sodium chloride (NaCl). The blue spheres represent Cl- ions, and the red spheres represent Na+ ions. The length of the cube edge is a = 0.562 737 nm.

Demo slits Using natural double slits or gratings Figure 37.7 Light intensity versus d sin  for a double-slit interference pattern when the screen is far from the two slits (L >> d).

NaCl crystals Microscopy Figure 38.26 Crystalline structure of sodium chloride (NaCl). The blue spheres represent Cl- ions, and the red spheres represent Na+ ions. The length of the cube edge is a = 0.562 737 nm. Microscopy

Figure 38. 26 Crystalline structure of sodium chloride (NaCl) Figure 38.26 Crystalline structure of sodium chloride (NaCl). The blue spheres represent Cl- ions, and the red spheres represent Na+ ions. The length of the cube edge is a = 0.562 737 nm. Fig 38-26, p.1225

X-ray diffraction Figure 38.26 Crystalline structure of sodium chloride (NaCl). The blue spheres represent Cl- ions, and the red spheres represent Na+ ions. The length of the cube edge is a = 0.562 737 nm.

X-ray diffraction of NaCl Figure 38.26 Crystalline structure of sodium chloride (NaCl). The blue spheres represent Cl- ions, and the red spheres represent Na+ ions. The length of the cube edge is a = 0.562 737 nm.

De Broglie – What did he say? Figure 38.26 Crystalline structure of sodium chloride (NaCl). The blue spheres represent Cl- ions, and the red spheres represent Na+ ions. The length of the cube edge is a = 0.562 737 nm.

Figure 38. 26 Crystalline structure of sodium chloride (NaCl) Figure 38.26 Crystalline structure of sodium chloride (NaCl). The blue spheres represent Cl- ions, and the red spheres represent Na+ ions. The length of the cube edge is a = 0.562 737 nm.

X-ray diffraction Electron diffraction Figure 38.26 Crystalline structure of sodium chloride (NaCl). The blue spheres represent Cl- ions, and the red spheres represent Na+ ions. The length of the cube edge is a = 0.562 737 nm.

Who else? Figure 38.26 Crystalline structure of sodium chloride (NaCl). The blue spheres represent Cl- ions, and the red spheres represent Na+ ions. The length of the cube edge is a = 0.562 737 nm.

Demo slits Any Danger for us? We are too heavy: l = h/mv Figure 37.7 Light intensity versus d sin  for a double-slit interference pattern when the screen is far from the two slits (L >> d).

At a beach in Tel Aviv, Israel, plane water waves pass through two openings in a breakwall. Notice the diffraction effect—the waves exit the openings with circular wave fronts, as in Figure 37.1b. Notice also how the beach has been shaped by the circular wave fronts. p.1178