Chapter 36

1. Chapter 36 Diffraction

2. Fresnel and Fraunhofer diffraction • According to geometric optics, a light source shining on an object in front of a screen will cast a sharp shadow. Surprisingly, this does not occur.

3. Diffraction from a single slit • The result is not what you might expect. Refer to Figure 36.3.

4. Dark fringes in single-slit diffraction • Consider Figure 36.4 below. • The figure illustrates Fresnel and Fraunhofer outcomes.

5. Fresnel or Fraunhofer? • The previous slide outlined two possible outcomes but didn’t set conditions to make a choice. • Figure 36.5 (below) outlines a procedure for differentiation.

6. Fraunhofer diffraction and an example of analysis • Figure 36.6 (at bottom left) is a photograph of a Fraunhofer pattern from a single slit. • Follow Example 36.1, illustrated by Figure 36.7 (at bottom right).

7. Q36.1 Light of wavelength l passes through a single slit of width a. The diffraction pattern is observed on a screen that is very far from from the slit. Which of the following will give the greatest increase in the angular width of the central diffraction maximum? A. Double the slit width a and double the wavelength l. B. Double the slit width a and halve the wavelength l. C. Halve the slit width a and double the wavelength l. D. Halve the slit width a and halve the wavelength l.

8. A36.1 Light of wavelength l passes through a single slit of width a. The diffraction pattern is observed on a screen that is very far from from the slit. Which of the following will give the greatest increase in the angular width of the central diffraction maximum? A. Double the slit width a and double the wavelength l. B. Double the slit width a and halve the wavelength l. C. Halve the slit width a and double the wavelength l. D. Halve the slit width a and halve the wavelength l.

9. Q36.2 In a single-slit diffraction experiment with waves of wavelength l, there will be no intensity minima (that is, no dark fringes) if the slit width is small enough. What is the maximum slit width a for which this occurs? A. a = l/2 B. a = l C. a = 2l D. The answer depends on the distance from the slit to the screen on which the diffraction pattern is viewed.

10. A36.2 In a single-slit diffraction experiment with waves of wavelength l, there will be no intensity minima (that is, no dark fringes) if the slit width is small enough. What is the maximum slit width a for which this occurs? A. a = l/2 B. a = l C. a = 2l D. The answer depends on the distance from the slit to the screen on which the diffraction pattern is viewed.

11. Intensity maxima in a single-slit pattern • The expression for peak maxima is iterated for the strongest peak. • Consider Figure 36.9 that shows the intensity as a function of angle.

12. Intensity from single slit • The approximation of sin θ= θ is very good considering the size of the slit and the wavelength of the light.

13. Multiple slit interference • The analysis of intensity to find the maximum is done in similar fashion as it was for a single slit.

14. Several slits • More slits produces sharper peaks

15. Q36.3 In Young’s experiment, coherent light passing through two slits separated by a distance d produces a pattern of dark and bright areas on a distant screen. If instead you use 10 slits, each the same distance d from its neighbor, how does the pattern change? A. The bright areas move farther apart. B. The bright areas move closer together. C. The spacing between bright areas remains the same, but the bright areas become narrower. D. The spacing between bright areas remains the same, but the bright areas become broader.

16. A36.3 In Young’s experiment, coherent light passing through two slits separated by a distance d produces a pattern of dark and bright areas on a distant screen. If instead you use 10 slits, each the same distance d from its neighbor, how does the pattern change? A. The bright areas move farther apart. B. The bright areas move closer together. C. The spacing between bright areas remains the same, but the bright areas become narrower. D. The spacing between bright areas remains the same, but the bright areas become broader.

17. A range of parallel slits, the diffraction grating • Two slits change the intensity profile of interference; many slits arranged in parallel fashion are a diffraction grating.

18. Diffraction grating • What is the first order diffraction peak (angle) for a grating with 600 slits per mm for red (700 nm) and violet (400nm) light? • By what angle is the rainbow spread out for this situation?

19. The grating spectrograph • A grating can be used like a prism, to disperse the wavelengths ofa light source. If the source is white light, this process is unremarkable, but if the source is built of discrete wavelengths,our adventure is now called spectroscopy. Chemical systems and astronomical entities have discrete absorption or emission spectra that contain clues to their identity and reactivity. See Figure 36.19 for a spectral example from a distant star.

20. The grating spectrograph II—instrumental detail • Spectroscopy (the study of light with a device such as the spectrograph shown below) pervades the physical sciences.

21. X-ray diffraction • X-rays have a wavelength commensurate with atomic structure. Rontgen had only discovered this high-energy EM wave a few decades earlier when Friederich, Knipping, and von Laue used it to elucidate crystal structures between adjacent ions in salt crystals. The experiment is shown below in Figure 36.21.

22. Ionic configurations from x-ray scattering • Arrangements of cations and anions in salt crystals (like Na+ and Cl– in Figure 36.22 … not shown) can be discerned from the scattering pattern they produced when irradiated by x-rays.

23. X-ray scattering set Watson and Crick to work • An x-ray scattering pattern recorded by their colleague Dr. Franklin led Watson and Crick to brainstorm the staircase arrangement that eventually led to the Nobel Prize. • Follow Example 36.5, illustrated by Figure 36.25 below.

24. Circular apertures and resolving power • In order to have an undistorted Airy disk (for whatever purpose), wavelength of the radiation cannot approach the diameter of the aperture through which it passes. Figures 36.26 and 36.27 illustrate this point.

25. Using multiple modes to observe the same event • Multiple views of the same event can “nail down” the truth in the observation. • Follow Example 36.6, illustrated by Figure 36.29.

26. Holography—experimental • By using a beam splitter, coherent laser radiation can illuminate an object from different perspective. Interference effects provide the depth that makes a three-dimensional image from two-dimensional views. Figure 36.30 illustrates this process.

27. Holography—theoretical • The wavefront interference creating the hologram is diagrammed in Figure 36.31 below.

28. Holography—an example • Figure 36.32 shows a holographic image of a pile of coins. You can view a hologram from nearly any perspective you choose and the “reality” of the image is astonishing.