Using two models in optics: Students’ difficulties and suggestions for teaching

See, for example,

I.

Galili

, “,” (), – ();

I.

Galili

and

A.

Hazan

, “,” (), – ();

F.

Goldberg

and

L. C.

McDermott

, “,” (), – ();

K.

Wosilait

,

P. R. L.

Heron

,

P. S.

Shaffer

, and

L. C.

McDermott

, “,” (), – ().

J. Dunin-Borkowski, “Crooked Paths of Straight Rays,” in Proceedings of International Conference on Physics Education GIREP’93, Minho University, Braga, Portugal, 16–21 July 1993, edited by L. C. Pereira, J. A. Ferreira, and H. A. Lopes (1994), pp. 333–337.

G. Verkerk and R. E. A. Bouwens, “Learning Optics from Seeing Light,” in Proceedings of International Conference on Physics Education GIREP’93, Minho University, Braga, Portugal, 16–21 July 1993, edited by L. C. Pereira, J. A. Ferreira, and H. A. Lopes (1994), pp. 100–121.

C. Taylor, “Images, Optics and Education,” in Proceedings of International Conference on Physics Education GIREP’93, Minho University, Braga, Portugal, 16–21 July 1993, edited by L. C. Pereira, J. A. Ferreira, and H. A. Lopes (1994), pp. 122–136.

(a) L. Maurines, “Students and the Wave-geometrical Model of the Propagation of Waves in a Three Dimensional Medium,” in Research in Science Education in Europe, edited by M. Bandiera et al. (Kluwer Academic, Dordrecht, The Netherlands, 1999), pp. 103–112;

(b) L. Maurines, “Spontaneous Reasoning on Light Diffraction and Coherent Illumination Optical Imaging,” in Proceedings of the Second International Conference of the European Science Education Research Association (ESERA), Research in Science Education. Past, Present and Future, 31 August–4 September 1999, Kiel, Germany, edited by M. Komorek, H. Behrendt, H. Dahncke, R. Duit, W. Gräber, and A. Kross (1999), Vol. 1, pp. 92–94.

For instance, Maurines (Ref. 5) considers as incorrect some students’ answers which state that, when a nondiffracting diaphragm is placed in front of a lens and illuminated by a plane wave, this diaphragm has no optical image, whereas it can be argued that nothing special happens in the conjugate image plane of such a diaphragm. Nothing changes on the screen when the diaphragm is moved. Is this observation compatible with the understanding of image formation and the part of the lens as an imaging system?

B. S.

Ambrose

,

P. S.

Shaffer

,

R. N.

Steinberg

, and

L.

McDermott

, “,” (), – ();

K.

Wosilait

,

P. R. L.

Heron

,

P. S.

Shaffer

, and

L. C.

McDermott

, “,” (), – ().

P. Colin, “Two Models for a Physical Situation: The Case of Optics. Student’s Difficulties, Teachers’ Viewpoints and Guidelines for a Didactical Structure,” in Selected Papers from the Second International Conference of the European Science Education Research Association (ESERA), Kiel, Germany (Kluwer Academic, Dordrecht, The Netherlands, 2001) pp. 241–246 (to be published);

P. Colin, “Two Models for a Physical Situation: The Case of Optics. Student’s Difficulties, Teachers’ Viewpoints and Guidelines for a Didactical Structure,” in Proceedings of the Second International Conference of the European Science Education Research Association (ESERA), Research in Science Education. Past, Present and Future, 31 August–4 September 1999, Kiel, Germany, edited by M. Komorek, H. Behrendt, H. Dahncke, R. Duit, W. Gräber, and A. Kross (1999), Vol. 2, pp. 143–145;

P. Colin, “Two Models for a Physical Situation: The Case of Optics. Student’s Difficulties, Teachers’ Viewpoints and Guidelines for a Didactical Structure,” in 4th European Science Education Summerschool, Marly le Roi, France, 26 August–2 September 1998, edited by M. Méheut and G. Rebmann (Université Denis Diderot, Paris, 1999), pp. 134–137;

P.

Colin

and

L.

Viennot

, “,” , , – ().

This definition of an “image” should not be confused with the pattern of illumination, called “geometric image” by Wosilait et al. (see Ref. 1), observed on a screen when an aperture is located between the light source and the viewing screen.

In order to justify that the optical paths between plane Π and point M are all equal, the reversibility of paths of light could be used. As shown in Fig. 4, a point source located at M emits a spherical wave transformed into a plane wave by the lens. But it should be stressed that in such a case, the field in the plane where the holes are located is very different from the situation considered in Fig. 3.

STTIS (“Science Teacher Training in an Information Society”) Symposium, “The innovative use of symbolic representations and informatic tools,” in Proceedings of the Second International Conference of the European Science Education Research Association (ESERA), Research in Science Education. Past, Present and Future, 31 August–4 September 1999, Kiel, Germany, edited by M. Komorek, H. Behrendt, H. Dahncke, R. Duit, W. Gräber, and A. Kross (1999), Vol. 2, pp. 623–636.

See, for instance,

L. C.

Mc Dermott

and

P. S.

Schaffer

, “,” , – ().

See Ref. 10.

P. Colin, “Passage de l’optique géométrique à l’optique ondulatoire: l’idée de sélection par l’aval de l’information” [Unpublished report “Mémoire de tutorat,” Université Paris 7-Denis Diderot (on request from LDSP)] (1997).

M. Bertin, J. P. Faroux, and J. Renault, Optique et physique ondulatoire. Optique géométrique et optique physique. Phénomènes de propagation (Cours de physique, Marketing, Paris, 1986), 3rd éd., pp. 221–224.

Huygens’ principle should be carefully used, so as not to confuse secondary sources of wavelets with classic incoherent point sources of geometrical optics. Thus, it is the status of the Huygens sources which is under discussion and, consequently, the status of the “object.” If the existence of fringes before the lens is admitted, which is not evident because no sensors are located at this place to detect them, these fringes cannot be considered as a “classical” object whose image is given by the lens. See below for further developments.

R. Duffait, Expériences d’optique, Agrégation de Sciences Physiques (Bréal, Paris, 1997), p. 62.

Concerning the students’ story-like analysis, see

S.

Rozier

and

L.

Viennot

, “,” (), – ();

see also Refs. 14 and 5.

G. Kress and T. van Leeuwen, Reading Images: the Grammar of Visual Design (Routledge and Kegan Paul, London, 1996).

See Ref. 8.

See Ref. 12.

For instance, in a photographic camera, it is the location of the film (with respect to the lens) that determines the elements of the scene which will be seen sharply on the photograph.

Although “light rays” are commonly used, there is no consensus about their definition (see D. S. Goodmann, “General Principles of Geometric Optics,” in Handbook of Optics, edited by M. Bass (McGraw-Hill, New York, 1995), Vol. I, pp. 3–109. Rays are often defined as lines drawn in space corresponding to the direction of the energy flow, more precisely, to the surface density of the power flow, i.e., to the Poynting vector. They are perpendicular to the surfaces of constant phase in a homogeneous medium, when these surfaces can be well-defined. What should be stressed is that “paths for (the calculation of) phase” should not be confused with routes for energy of the resultant field (see Ref. 14).

See, for example,

F.

Goldberg

and

L. C.

McDermott

, “,” (), – ().