Chapter 27 diffraction and waves interaction

physics for university students

1. Physics Eleventh Edition Cutnell & Johnson Chapter 27 Interference and the Wave Nature of Light

2. 27.1 The Principle of Linear Superposition (1 of 3) When two or more light waves pass through a given point, their electric fields combine according to the principle of superposition. 2 Copyright ©2018 John Wiley & Sons, Inc. which states that the resultant disturbance is the sum of the disturbances from the individual waves Light is also a wave , an electromagnetic wave, and it too obeys the superposition principle. When two or more light waves pass through a given point, their electric fi elds combine according to the principle of linear superposition and produce a resultant electric field

3. 27.1 The Principle of Linear Superposition (1 of 3) The waves emitted by the sources start out in phase and arrive at point P in phase, leading to constructive interference . 3 Copyright ©2018 John Wiley & Sons, Inc.

4. 27.1 The Principle of Linear Superposition (2 of 3) The waves emitted by the sources start out in phase and arrive at point P out of phase, leading to destructive interference. 4 Copyright ©2018 John Wiley & Sons, Inc.

5. 27.1 The Principle of Linear Superposition (3 of 3) If constructive or destructive interference is to continue ocurring at a point, the sources of the waves must be coherent sources . Two sources are coherent if the waves they emit maintain a constant phase relation. 5 Copyright ©2018 John Wiley & Sons, Inc.

6. 27.2 Young’s Double Slit Experiment (1 of 7) In Young’s experiment, two slits acts as coherent sources of light. Light waves from these slits interfere constructively and destructively on the screen. 6 Copyright ©2018 John Wiley & Sons, Inc.

7. 27.2 Young’s Double Slit Experiment (1 of 7) In May of 1801, while pondering some of Newton's experiments, Young came up with the basic idea for the now-famous double-slit experiment to  demonstrate the interference of light waves . The demonstration would provide solid evidence that light was a wave, not a particle Young's double-slit experiment  uses two coherent sources of light placed at a small distance apart . Usually, only a few orders of magnitude greater than the wavelength of light are used. Young's double-slit experiment helped in understanding the wave theory of light , which is explained with the help of a diagram. 7 Copyright ©2018 John Wiley & Sons, Inc.

8. 27.2 Young’s Double Slit Experiment (1 of 7) What is the significance of monochromatic wave used in Young's double-slit experiment? Every color produces its own pattern, with a spacing between the maxima that is characteristic of the wavelength. With several colors, the patterns are superimposed, and it is difficult to pick out a single maximum. Using monochromatic light,  we can eliminate this problem 8 Copyright ©2018 John Wiley & Sons, Inc.

9. 27.2 Young’s Double Slit Experiment (2 of 7) The waves coming from the slits interfere constructively or destructively, depending on the difference in distances between the slits and the screen. 9 Copyright ©2018 John Wiley & Sons, Inc.

10. 27.2 Young’s Double Slit Experiment (3 of 7) 10 Copyright ©2018 John Wiley & Sons, Inc.

11. 27.2 Young’s Double Slit Experiment (4 of 7) Bright fringes of a double-slit Dark fringes of a double-slit 11 Copyright ©2018 John Wiley & Sons, Inc.

12. 27.2 Young’s Double Slit Experiment (5 of 7) Example 1 Young’s Double-Slit Experiment Red light (664 nm) is used in Young’s experiment with slits separated by 0.000120 m. The screen is located a distance 2.75 m from the slits. Find the distance on the screen between the central bright fringe and the third-order bright fringe. 12 Copyright ©2018 John Wiley & Sons, Inc.

13. 27.2 Young’s Double Slit Experiment (6 of 7) 13 Copyright ©2018 John Wiley & Sons, Inc.

14. 27.2 Young’s Double Slit Experiment (7 of 7) Conceptual Example 2 White Light and Young’s Experiment The figure shows a photograph that illustrates the kind of interference fringes that can result when white light is used in Young’s experiment. Why does Young’s experiment separate white light into its constituent colors? In any group of colored fringes, such as the two singled out, why is red farther out from the central fringe than green is? Why is the central fringe white? 14 Copyright ©2018 John Wiley & Sons, Inc.

15. 27.5 Diffraction (1 of 7) Diffraction is the bending of waves around obstacles or the edges of an opening. Huygens’ principle Every point on a wave front acts as a source of tiny wavelets that move forward with the same speed as the wave; the wave front at a later instant is the surface that is tangent to the wavelets. 15 Copyright ©2018 John Wiley & Sons, Inc. Sound bends, or diffracts, around the edges of a doorway, so even a person who is not standing directly in front of the opening can hear the sound. The five red points within the doorway act as sources and emit the five Huygens wavelets shown in red.

16. 27.5 Diffraction (2 of 7) The extent of the diffraction increases as the ratio of the wavelength to the width of the opening increases. 16 Copyright ©2018 John Wiley & Sons, Inc.

17. 27.5 Diffraction (3 of 7) 17 Copyright ©2018 John Wiley & Sons, Inc.

18. 27.5 Diffraction (4 of 7) This top view shows five sources of Huygens’ wavelets. 18 Copyright ©2018 John Wiley & Sons, Inc.

19. 27.5 Diffraction (5 of 7) These drawings show how destructive interference leads to the first dark fringe on either side of the central bright fringe. 19 Copyright ©2018 John Wiley & Sons, Inc.

20. 27.5 Diffraction (6 of 7) Dark fringes for single slit diffraction 20 Copyright ©2018 John Wiley & Sons, Inc.

21. 27.5 Diffraction (6 of 7) 21 Copyright ©2018 John Wiley & Sons, Inc.

22. 22 Copyright ©2018 John Wiley & Sons, Inc. Reasoning: The width of the central bright fringe is determined by two factors. One is the angle 𝜃 that locates the first dark fringe on either side of the midpoint. The other is the distance L between the screen and the slit. Larger values for 𝜃 and L lead to a wider central bright fringe. Larger values of 𝜃 mean greater diffraction and occur when the ratio 𝜆/W is larger. Thus, we expect the width of the central bright fringe to be greater when the slit width W is smaller. The angle 𝜃 locates the first dark fringe when m = 1: sin 𝜃 = (1) 𝜆/W. Therefore, θ = 4.7° According to Figure 27.23, tan 𝜃 = y/L, so the width 2y of the central bright fringe is 2y = 2L tan θ = 2 (0.40 m) tan 4.7° = 0.066 m b) Repeating the same calculations as in part (a) with W = 2.5 × m reveals that 2y = 0.13 m . As expected for a given wavelength, the width 2y of the central maximum in the diffraction pattern is greater when the width of the slit is smaller  

23. 23 Copyright ©2018 John Wiley & Sons, Inc.

24. 27.5 Diffraction (7 of 7) 24 Copyright ©2018 John Wiley & Sons, Inc.

25. 27.6 Resolving Power (1 of 5) Three photographs of an automobile’s headlights, taken at progressively greater distances. 25 Copyright ©2018 John Wiley & Sons, Inc.

26. 27.6 Resolving Power (2 of 5) First minimum of a circular diffraction pattern 26 Copyright ©2018 John Wiley & Sons, Inc.

27. 27.6 Resolving Power (3 of 5) 27 Copyright ©2018 John Wiley & Sons, Inc.

28. 27.6 Resolving Power (4 of 5) Rayleigh criterion Two point objects are just resolved when the first dark fringe in the diffraction pattern of one falls directly on the central bright fringe in the diffraction patter of the other. 28 Copyright ©2018 John Wiley & Sons, Inc.

29. 27.6 Resolving Power (5 of 5) Conceptual Example 8 What You See is Not What You Get The French postimpressionist artist Georges Seurat developed a technique of painting in which dots of color are placed close together on the canvas. From sufficiently far away the individual dots are not distinguishable, and the images in the picture take on a more normal appearance. Why does the camera resolve the dots, while his eyes do not? 29 Copyright ©2018 John Wiley & Sons, Inc.

30. 27.7 The Diffraction Grating (1 of 5) An arrangement consisting of a large number of closely spaced, parallel slits is called a diffraction grating . 30 Copyright ©2018 John Wiley & Sons, Inc.

31. 27.7 The Diffraction Grating (2 of 5) The conditions shown here lead to the first- and second-order intensity maxima in the diffraction pattern. 31 Copyright ©2018 John Wiley & Sons, Inc.

32. 27.7 The Diffraction Grating (3 of 5) The bright fringes produced by a diffraction grating are much narrower than those produced by a double slit. Principal maxima of a diffraction grating 32 Copyright ©2018 John Wiley & Sons, Inc.

33. 27.7 The Diffraction Grating (4 of 5) Example 9 Separating Colors With a Diffraction Grating A mixture of violet (410 nm) light and red (660 nm) light falls onto a grating that contains For each wavelength, find the angle that locates the first-order maximum. 33 Copyright ©2018 John Wiley & Sons, Inc.

34. 27.7 The Diffraction Grating (5 of 5) 34 Copyright ©2018 John Wiley & Sons, Inc.

35. 27.8 Compact Discs, Digital Video Discs, and the Use of Interference (1 of 2) 35 Copyright ©2018 John Wiley & Sons, Inc.

36. 27.8 Compact Discs, Digital Video Discs, and the Use of Interference (2 of 2) 36 Copyright ©2018 John Wiley & Sons, Inc.

37. 27.9 X-Ray Diffraction (1 of 2) 37 Copyright ©2018 John Wiley & Sons, Inc.

38. 27.9 X-Ray Diffraction (2 of 2) 38 Copyright ©2018 John Wiley & Sons, Inc.

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