Brasil Final Report - Department of Physics - The Ohio State University

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the modern physics course, the students had reviewed this material and covered similar topics in the
context of matter waves. The interviews, from 3/4 to 1 hour in length, were videotaped.
The students were shown a small bulb, a screen, and a mask with a rectangular aperture 1 cm
wide and 3 cm tall. (See Fig. 2.) They were asked to predict what they would see on the screen and
how this would change as the aperture is gradually narrowed to become a slit. Initially, the
geometric image of the aperture would be seen. Eventually, a single-slit diffraction pattern would
appear. 11
Identification of difficulties
The difficulties revealed by the written questions and interviews were similar. Among the
introductory students, there was a tendency to use a hybrid model with features of both geometrical
and physical optics. For example, some students seemed to believe that light passing through the
center of the slit forms a geometric image, while light striking the edges of the slit is bent to form
other bright regions on the screen. [See Fig. 3(a).] Some modern physics students expressed a
similar belief but used a hybrid model that incorporated photons. [See Fig. 3(b).] Their exposure to
more advanced material seems to have introduced additional difficulties.
Students often misused comparisons between slit width and wavelength or amplitude. Many
considered diffraction to be a consequence of whether or not light could “fit” though the slit.
Among the introductory students, some claimed that if the slit width were greater than the wave
amplitude, light would be able to pass through the slit but that if the slit width were less, no light
could emerge. [See Fig. 3(c).] For these students, the amplitude of a wave had a spatial extent. The
modern physics students carried some of the same ideas a step further by introducing photons
distributed along sinusoidal paths. [See Fig. 4(a) and 4(b).] The diagrams that they drew indicated
that the photons would not get through the slit if the amplitude of the wave were greater than the
slit width.
Underlying the specific difficulties illustrated above was a more basic difficulty. Students often
failed to relate diffraction effects to differences in path length (ΔD) or phase (Δφ). They had not
developed a basic wave model that they could use to account for the diffraction of light through a
narrow slit in the far-field limit.
Comparison of performance on quantitative and qualitative questions
As can be seen from Table I, student performance on the qualitative question was much poorer
than on the quantitative question. Even the students (N ~ 130) who had previously been given the
quantitative question had difficulty with the qualitative question. When explanations were ignored,
the success rate was about 45%. When explanations were considered, this percentage dropped to
approximately 10%. These results support the following generalizations related to learning and
teaching (in italics). 12
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Facility in solving standard quantitative problems is not an adequate criterion for functional
understanding. Questions that require qualitative reasoning and verbal explanation are
essential for assessing student learning.
The investigator tried to ensure, either tacitly or overtly, that certain simplifying assumptions would be made.
If the students seemed to think of the bulb as an extended source, they were told to treat it as a point source. If they
recognized that the light would be composed of many colors, they were told to imagine a red bulb.