Our process of didactic transposition: presentation of the teaching unit and its
construction
1. Identification of the academic knowledge of geometric optics
The academic knowledge of geometric optics was identified both from (Alonso & Finn,
1992; Born & Wolf, 1980; Hecht, 1987; Jenkins & White, 1957; Ronchi, 1991) and from
our own knowledge on the subject matter.
Vision; Image (real, virtual, production of, using ray-tracing technics; upward and
inverted image); light (nature of, propagation, source of, dispersion, white; ray of;
paraxial rays; spectrum of; division of the spectrum; wavelength; frequency; energy);
bodies (opaque, translucent); Shadows; law of reflection (working examples; specular
and diffuse); law of refraction (working examples; specular and diffuse; index of
refraction; comparative values of index of refraction for water, air and glass); Snell’s law;
Total reflection (critical angle; working examples); mirrors (plane, spherical, focal points;
mirror equations); lens (thin lens, diverging, converging, focal points, used to correct
myopia and astigmatism, lensmaker’s equation); prism (dispersion of white light by);
colour (additive and subtractive rule, dispersion of white light and); rainbow; flux of light;
illuminance.
2. Elementarization of academic knowledge of Geometric optic (e.g., Duit,
Gropengießer, Kattmann, Komorek, & Parchmann, 2012, pp. 18-22)
The vision process and eyes anatomy;
Light as an entity that travel in space from a source with a speed far away of human
experience;
Image and image formation by convergent lens and concave mirrors
Atmosphere as the optical medium in which much of the optical phenomena occur (we
do not live in empty space)
Laws of reflection and refraction (qualitative aspects)
Instruments and its use: mirrors, lens, prism
Dispersion of white light by a prism
Colours
3. Construction of the Knowledge-to-be-taught
First theoretical lesson: (1h 45 min)
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In optics the observer must be taken in account.
Integrate Light propagation, anatomy of the eye, light refraction in the biological
lens and formation of an inverted image in the sensible part of the eye, the retina.
Explanation of the law of refraction in a qualitative approach.
Ascribe to cornea plus crystalline humour the function of a convex lens. (working
out this in a diagrammatical way using Kepler’s cone represent light propagation)
First laboratory lesson: 2x (1h30 min) (the class was divided into two)
-
-
Recognise evidences of rectilinear propagation of light in the same optical
medium (Shadows as the absence of light; LASER light in a container with a
colloidal substance)
The atmosphere and influence in optical phenomena
Illustrate the schema of the eye ball.
Discern lens biconcave from lens biconvex.
Second theoretical lesson: (1h 45 min)
-
-
Light representation in the geometrical optics as a model that represent the
direction of its propagation and say nothing on its nature (use of models in
science).
light flux
Thin lens approximation (a model very useful);
Explanation of the law of reflection (introducing specular reflection and diffuse
one)
The connection between refraction and light dispersion
Explain the colour as a result of light dispersion.
Second lab lesson 2x (1h 30 min)
-
Working out light dispersion in diverse circumstances, including with a prism.
Classify lens and see the behaviour of light in concave and convex lens.
Magnifying glass and its correct use;
Identify the correct lens to use in order to obtain an image in a cardboard.
Third theoretical lesson (1h 45 min)
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Explain the phenomena of Total reflection
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Explain the rainbow
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Interpret the myopia and farsightedness as the result of physical processes and
identify appropriate lens to correct them;
-
Undulatory theory of light: a brief introduction: what is a wave (transversal and
longitudinal waves and examples), wavelength, frequency and their relation.
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Electromagnetic spectrum. Utility if each zone.
-
Orders of magnitude of wavelength and frequency of visible light, radio waves,
microwaves and x-rays, between others
Third lab lesson 2x (1h30 min)
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Identify and classify mirrors;
-
Generate real image of a candle in a cardboard using concave mirrors
-
Generate colours adding coloured lights.
Forth lab lesson (between the third and four laboratory lesson students had the first
theoretical lesson on astronomy) 2x (1h 30 min)
-
Generate colours by light subtraction (subtractive synthesis
-
Interpret the appearances of coloured shadows
1. Identification of the academic
knowledge of geometric optics
Didactic Transposition
2. Elementarization of academic
knowledge of Geometric optic
3. Construction of the
Knowledge-to-be-taught