Comparing different approaches to visualizing light waves: An experimental study on teaching wave optics

Abstract

Research has shown that students have tremendous difficulties developing a qualitative understanding of wave optics, at all educational levels. In this study, we investigate how three different approaches to visualizing light waves affect students' understanding of wave optics. In the first, the conventional, approach light waves are represented by sinusoidal curves. The second teaching approach includes representing light waves by a series of static images, showing the oscillating electric field vectors at characteristic, subsequent instants of time. Within the third approach phasors are used for visualizing light waves. A total of N ¼ 85 secondary school students were randomly assigned to one of the three teaching approaches, each of which lasted a period of four class hours. Students who learned with phasors and students who learned from the series of static images outperformed the students learning according to the conventional approach, i.e., they showed a much better understanding of basic wave optics, as measured by a conceptual survey administered to the students one week after the treatment. Our results suggest that visualizing light waves with phasors or oscillating electric field vectors is a promising approach to developing a deeper understanding of wave optics for students enrolled in conceptual level physics courses.

A proposal for a new symbolism to indicate phasors

“…A first survey on the acceptance of the new notation was performed by submitting a very simple questionnaire to a (still limited) number of students (N = 25); the obtained outcomes testify the good impact that it would have both on the understanding of the main properties of a phasor (and this would be at least in qualitative agreement with [23]) and on the approach to the solution of problems involving, in particular, circuits in alternating current.…”

“…From the educational point of view, after the work of Worland and Moelter [14], the effectiveness of using phasors for teaching wave optics has been recently probed by Mesic et al [23]. In the latter work, the authors instructed 16-years old high school students about wave optics by using three different approaches: a conventional one, in which the light waves are represented by sinusoidal curves and interference phenomena are seen as "adding multiple curves"; a "sequence of electric vectors (SEV)" approach, using oscil-lating electric field vectors for representing light wave, and finally the phasor approach.…”

“…In the latter work, the authors instructed 16-years old high school students about wave optics by using three different approaches: a conventional one, in which the light waves are represented by sinusoidal curves and interference phenomena are seen as "adding multiple curves"; a "sequence of electric vectors (SEV)" approach, using oscil-lating electric field vectors for representing light wave, and finally the phasor approach. It is worth noting that the best performances in the understanding of wave optics have been reached by students instructed with the phasor approach [23]. In Ref.…”

“…In Ref. [23] it is also pointed out that, even if the use of phasors fulfills almost all the criteria on effective visualization of wave optics phenomena, this approach is currently avoided by several textbooks both at high school or university level. As an example, even in some well-known advanced textbook (e.g.…”

Measuring students’ conceptual understanding of wave optics: A Rasch modeling approach

“…Such a mechanicistic reasoning is also reflected in the erroneous belief that reducing wavelength results in reducing of other "dimensions of the wave" [19]. Sometimes students also struggle with distinguishing the spatial and temporal versions of sinusoidal representations of a light wave which is probably a difficulty that has its origins in the mere characteristics of traditional wave optics instruction [20]. Besides difficulties in interpreting representations of light waves, students often fail to correctly apply the Huygens principle, although they know to verbally reproduce it.…”