An investigation of student understanding of single-slit diffraction and double-slit interference

American Journal of Physics

Volumn 67, Issue 2, 1999, Pages 146-155

  Ambrose, Bradley S ^b   Shaffer, Peter S ^b   Steinberg, Richard N ^a,b   McDermott, Lillian C ^b  

^a Bldg 142   (United States)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033433205     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.19210     Document Type: Article

References (25)

1. F. M. Goldberg and L. C. McDermott, "An investigation of student understanding of the real image formed by a converging lens or concave mirror," Am. J. Phys. 55, 108-119 (1987); "Student difficulties in understanding image formation by a plane mirror," Phys. Teach. 11, 472-480 (1986).
2. F. M. Goldberg and L. C. McDermott, "An investigation of student understanding of the real image formed by a converging lens or concave mirror," Am. J. Phys. 55, 108-119 (1987); "Student difficulties in understanding image formation by a plane mirror," Phys. Teach. 11, 472-480 (1986).
3. K. Wosilait, P. R. L. Heron, P. S. Shaffer, and L. C. McDermott, "Development and assessment of a research-based tutorial on light and shadow," Am. J. Phys. (to be published).
4. K. Wosilait, "Research as a guide for the development of tutorials to improve student understanding of geometrical and physical optics," Ph.D. dissertation, Department of Physics, University of Washington, 1996 (unpublished).
5. B. S. Ambrose, "Investigation of student understanding of the wave-like properties of light and matter," Ph.D. dissertation, Department of Physics. University of Washington, 1998 (unpublished).
6. Other papers that report on our research and curriculum development in physical optics include: K. Wosilait, P. R. L. Heron, P. S. Shaffer, and L. C. McDermott, "Addressing student difficulties in applying a wave model to the interference and diffraction of light" (submitted for publication); B. S. Ambrose, P. R. L. Heron, S. Vokos, and L. C. McDermott, "Student understanding of common representations of light as an electromagnetic wave" (submitted for publication).
7. Other papers that report on our research and curriculum development in physical optics include: K. Wosilait, P. R. L. Heron, P. S. Shaffer, and L. C. McDermott, "Addressing student difficulties in applying a wave model to the interference and diffraction of light" (submitted for publication); B. S. Ambrose, P. R. L. Heron, S. Vokos, and L. C. McDermott, "Student understanding of common representations of light as an electromagnetic wave" (submitted for publication).
8. L. C. McDermott, P. S. Shaffer, and the Physics Education Group at the University of Washington, Tutorials in Introductory Physics, Preliminary Edition (Prentice Hall, Upper Saddle River, NJ, 1998). The research reported in this paper has guided the development and assessment of several tutorials on optics.
9. Research by our group on geometrical optics has also guided the development of a laboratory-based curriculum intended for the preparation of precollege teachers, for underprepared students, and for liberal arts majors. See L. C. McDermott and the Physics Education Group at the University of Washington, Physics by Inquiry (Wiley, New York, 1996), Vois. I and II.
10. For descriptions of how the Physics Education Group conducts research on student understanding of physics, see Refs. 1-5, 13, and 17. Also, sec D. E. Trowbridge and L. C. McDermott, "Investigation of student understanding of the concept of velocity in one dimension," Am. J. Phys. 48, 1020-1028 (1980); "Investigation of student understanding of the concept of acceleration in one dimension," ibid. 49, 242-253 (1981); L. C. McDermott and P. S. Shaffer. "Research as a guide to curriculum development: An example from introductory electricity. Part I. Investigation of student understanding," ibid. 60, 994-1003 (1992); Erratum to Part I, 61, 81 (1993).
11. For descriptions of how the Physics Education Group conducts research on student understanding of physics, see Refs. 1-5, 13, and 17. Also, sec D. E. Trowbridge and L. C. McDermott, "Investigation of student understanding of the concept of velocity in one dimension," Am. J. Phys. 48, 1020-1028 (1980); "Investigation of student understanding of the concept of acceleration in one dimension," ibid. 49, 242-253 (1981); L. C. McDermott and P. S. Shaffer. "Research as a guide to curriculum development: An example from introductory electricity. Part I. Investigation of student understanding," ibid. 60, 994-1003 (1992); Erratum to Part I, 61, 81 (1993).
12. For descriptions of how the Physics Education Group conducts research on student understanding of physics, see Refs. 1-5, 13, and 17. Also, sec D. E. Trowbridge and L. C. McDermott, "Investigation of student understanding of the concept of velocity in one dimension," Am. J. Phys. 48, 1020-1028 (1980); "Investigation of student understanding of the concept of acceleration in one dimension," ibid. 49, 242-253 (1981); L. C. McDermott and P. S. Shaffer. "Research as a guide to curriculum development: An example from introductory electricity. Part I. Investigation of student understanding," ibid. 60, 994-1003 (1992); Erratum to Part I, 61, 81 (1993).
13. For descriptions of how the Physics Education Group conducts research on student understanding of physics, see Refs. 1-5, 13, and 17. Also, sec D. E. Trowbridge and L. C. McDermott, "Investigation of student understanding of the concept of velocity in one dimension," Am. J. Phys. 48, 1020-1028 (1980); "Investigation of student understanding of the concept of acceleration in one dimension," ibid. 49, 242-253 (1981); L. C. McDermott and P. S. Shaffer. "Research as a guide to curriculum development: An example from introductory electricity. Part I. Investigation of student understanding," ibid. 60, 994-1003 (1992); Erratum to Part I, 61, 81 (1993).
14. The term geometric image refers to the bright region on a screen that would be produced by the rectilinear propagation of light from a source through an aperture to the screen. For a discussion of the differences between this type of image and the real image formed by a converging lens, see F. Goldberg, S. Bendall, and I. Galili, "Lenses, pinholes, screens, and the eye," Phys. Teach. 29, 221-224 (1991).
15. In an introductory course, interactions between the electromagnetic waves and the material of which the slit edges are made are not considered. A more rigorous approach can be found in S. G. Lipson, H. Lipson, and D. S. Tannhauser, Optical Physics (Cambridge U.P., Cambridge, UK, 1995).
16. Edge diffraction is not typically emphasized in the course, although it is mentioned briefly in some texts and by some instructors during lecture.
17. The students were not expected to recognize that the axis of polarization of the light has an effect on the diffraction pattern. For a discussion of how the polarization of light can change the diffraction pattern, see T. W. Mayes and B. F. Melton, "Fraunhofer diffraction of visible light," Am. J. Phys. 62, 397-403 (1994); T. J. Racey, P. Rochon, and N. Gauthier, "Effect of light polarization on the diffraction pattern of small wires," ibid. 53, 783-786 (1985).
18. The students were not expected to recognize that the axis of polarization of the light has an effect on the diffraction pattern. For a discussion of how the polarization of light can change the diffraction pattern, see T. W. Mayes and B. F. Melton, "Fraunhofer diffraction of visible light," Am. J. Phys. 62, 397-403 (1994); T. J. Racey, P. Rochon, and N. Gauthier, "Effect of light polarization on the diffraction pattern of small wires," ibid. 53, 783-786 (1985).
19. This difficulty and others related to student beliefs about photons are discussed in R. N. Steinberg, G. E. Oberem, and L. C. McDermott, "Development of a computer-based tutorial on the photoelectric effect," Am. J. Phys. 64, 1370-1379 (1996).
20. Another explanation, not usually presented in introductory courses, is based on Feynman's path integral approach. In this formulation, all paths between the emitter and a point on the screen are ascribed a phase. The sum of the contributions of all paths yields the standard intensity pattern. See R. P. Feynman, QED, The Strange Theory of Light and Matter (Princeton U.P., Princeton, NJ, 1985).
21. For a description of a demonstration of a low-intensity, double-slit interference experiment, see S. Parker, "Single-photon double-slit interference-A demonstration," Am. J. Phys. 40, 1003-1007 (1972). An explanation intended for a first course in modern physics can be found in P. A. Tipler, Modern Physics (Worth, New York, 1978), p. 185.
22. For a description of a demonstration of a low-intensity, double-slit interference experiment, see S. Parker, "Single-photon double-slit interference-A demonstration," Am. J. Phys. 40, 1003-1007 (1972). An explanation intended for a first course in modern physics can be found in P. A. Tipler, Modern Physics (Worth, New York, 1978), p. 185.
23. See the second paper in Ref. 5.
24. In addition to Refs. 2, 3, 4, and 13, see L. C. McDermott, P. S. Shaffer, and M. D. Somers, "Research as a guide for teaching introductory mechanics: An illustration in the context of the Atwood's machine," Am. J. Phys. 62, 46-55 (1994); T. O'Brien Pride, S. Vokos, and L. C. McDermott, "The challenge of matching learning assessments to teaching goals: An example from the work-energy and impulse-momentum theorems," ibid. 66, 147-157 (1998).
25. In addition to Refs. 2, 3, 4, and 13, see L. C. McDermott, P. S. Shaffer, and M. D. Somers, "Research as a guide for teaching introductory mechanics: An illustration in the context of the Atwood's machine," Am. J. Phys. 62, 46-55 (1994); T. O'Brien Pride, S. Vokos, and L. C. McDermott, "The challenge of matching learning assessments to teaching goals: An example from the work-energy and impulse-momentum theorems," ibid. 66, 147-157 (1998).