No Access Submitted: 09 February 1998 Accepted: 17 June 1998 Published Online: 20 January 1999
American Journal of Physics 67, 146 (1999); https://doi.org/10.1119/1.19210
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  • Department of Physics, Box 351560, University of Washington, Seattle, Washington 98195-1560
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  • Bradley S. Ambrose
  • Peter S. Shaffer
  • Richard N. Steinberg
  • Lillian C. McDermott
Results from an investigation of student understanding of physical optics indicate that university students who have studied this topic at the introductory level and beyond often cannot account for the pattern produced on a screen when light is incident on a single or double slit. Many do not know whether to apply geometrical or physical optics to a given situation and may inappropriately combine elements of both. Some specific difficulties that were identified for single and double slits proved to be sufficiently serious to preclude students from acquiring even a qualitative understanding of the wave model for light. In addition, we found that students in advanced courses often had mistaken beliefs about photons, which they incorporated into their interpretation of the wave model for matter. A major objective of this investigation was to build a research base for the design of a curriculum to help students develop a functional understanding of introductory optics.
  1. 1. F. M. Goldbergand 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); Google ScholarScitation, ISI
    F. M. Goldbergand L. C. McDermott, “Student difficulties in understanding image formation by a plane mirror,” Phys. Teach. 11, 472–480 (1986). , Google ScholarScitation
  2. 2. 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). Google Scholar
  3. 3. 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of geometrical and physical optics,” Ph.D. dissertation, Department of Physics, University of Washington, 1996 (unpublished). Google Scholar
  4. 4. 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wave-like properties of light and matter,” Ph.D. dissertation, Department of Physics, University of Washington, 1998 (unpublished). Google Scholar
  5. 5. 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); Google Scholar
    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). Google Scholar
  6. 6. 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. Google Scholar
  7. 7. 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), Vols. I and II. Google Scholar
  8. 8. For descriptions of how the Physics Education Group conducts research on student understanding of physics, see Refs. 12345, 13, and 17. Google Scholar
    Also, see D. E. Trowbridgeand L. C. McDermott, “Investigation of student understanding of the concept of velocity in one dimension,” Am. J. Phys. 48, 1020–1028 (1980); Google ScholarScitation, ISI
    D. E. Trowbridgeand L. C. McDermott, “Investigation of student understanding of the concept of acceleration in one dimension,” Am. J. Phys. 49, 242–253 (1981); , Google ScholarScitation, ISI
    L. C. McDermottand P. S. Shaffer, “Research as a guide to curriculum development: An example from introductory electricity. Part I. Investigation of student understanding,” Am. J. Phys. 60, 994–1003 (1992); , Google ScholarScitation
    L. C. McDermottand P. S. Shaffer, Erratum to Part I, Am. J. Phys. 61, 81 (1993). , Google ScholarScitation, ISI
  9. 9. 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). Google ScholarScitation
  10. 10. 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). Google Scholar
  11. 11. Edge diffraction is not typically emphasized in the course, although it is mentioned briefly in some texts and by some instructors during lecture. Google Scholar
  12. 12. 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. Mayesand B. F. Melton, “Fraunhofer diffraction of visible light,” Am. J. Phys. 62, 397–403 (1994); Google ScholarScitation
    T. J. Racey, P. Rochon, and N. Gauthier, “Effect of light polarization on the diffraction pattern of small wires,” Am. J. Phys. 53, 783–786 (1985). , Google ScholarScitation
  13. 13. 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). Google ScholarScitation, ISI
  14. 14. 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). Google Scholar
  15. 15. 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). Google ScholarScitation
    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. , Google Scholar
  16. 16. See the second paper in Ref. 5. Google Scholar
  17. 17. 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); Google ScholarScitation, ISI
    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,” Am. J. Phys. 66, 147–157 (1998). , Google ScholarScitation
  1. © 1999 American Association of Physics Teachers.