Kepler and the fundamental theorem of optics

Authors

DOI:

https://doi.org/10.5007/1808-1711.2021.e71458

Abstract

The article discusses the arguments with which Kepler demonstrates what we will call the fundamental theorem of optics. According to this theorem, a homocentric beam of light that passes through a transparent sphere, provided that the amplitude of the beam is small, is concentrated again at one point on the other side of the sphere. We show how the philosopher, using geometric analogies as paper tools and despite relying on both an imprecise law for refraction and certain approaches, came to an outcome that tradition incorporated as promising. Indeed, modern tradition incorporated the theorem by correcting what, in his view, were methodological errors.

Author Biography

Carlos Alberto Cardona, Universidad del Rosario

Profesor titular, Escuela de Ciencias Humanas, Universidad del Rosario, Bogotá, Colombia

References

Alhacén. (edit. 1572). De Aspectibus (I-IV). En F. Risner (Edit.), Opticae thesaurus Alhazeni Arabis libri septem… Item Vitellonis Thuringopoloni libri decem (pp. 1-288). Basile: Per episcopios.

Alhacén. (trad. en 2001). De Aspectibus (I-III). En A. M. Smith (Edit. y Trad.), Alhacen’s Theory of Visual Perception (pp. 1-816). Philadelphia: American Philosophical Society.

Aristóteles. (trad. en 2004). Problemas. Madrid: Editorial Gredos.

Bacon, R. (trad. en 1998b). De speculis comburentibus. En D. Lindberg (Edit. y Trad.), Roger Bacon’s Philosophy of Nature (pp. 271-341). South Bend, Ind: St. Augustine’s Press.

Buchdahl, G. (1972). Methodological Aspects of Kepler´s Theory of Refraction. Studies in History and Philosophy of Sciences, no. 3, pp. 265-298.

Dupré, S. (2007). Playing with images in a Dark Room Kepler´s Ludi inside the Camera Obscura. En W. Lefèvre, 2007, pp. 59-73.

Gibson, J. (1979/2015). The Ecological Approach to Visual Perception. New York: Psychology Press.

Grant, E. (edit.). (1974). A Source Book in Medieval Science. Cambridge (Mass): Harvard University Press.

Heeffer, A. (2014). Data-Driven Induction in Scientific Discovery: A Critical Assessment Based on Kepler´s Discoveries. En E. Weber, D. Wouters & J. Meheus (edit.). Logic, Reasoning and Rationality (pp. 59-76). Dordrecht: Springer.

Helmholtz, H. (1909/2005) (3ª ed.). Treatise on Physiological Optics (Volúmenes 1, 2 y 3). Mineola: Dover Publications, Inc. Trad. James P. C. Southhall.

Itard, J. (1957). Les lois de la refraction de la lumiere chez Kepler. Revue d´histoire des sciences et de leurs applications, vol. 10, No. 1, pp. 59-68.

Kepler, J. (1600/1988). Apologia pro Tychone contra Ursum. En N. Jardine (edit.), The Birth of History and Philosophy of Science. Kepler´s A Defence of Tycho against Ursus with essays on its provenace and significance. Cambridge: Cambridge University Press, pp. 85-207.

Kepler, J. (1604/2000) [Paralipomena]. Optics: Paralipomena to Witelo & Optical Part of Astronomy. Santa Fe: Green Lion Press. Trad. William H. Donahue.

Kepler, J. (1604/1939) [GW]. Ad Vitellionem Paralipomena Quibus Astronomiae pars Optica traditur. In Gesammelte Werke (GW), vol II; München: C. H. Beck´sche Verlagsbuchhandlung; ed. and comm. Franz Hammer.

Kepler, J. (1611/2008). Dioptrik. In Schriften zur Optik. Frankfurt: Verlag Harri Deutch.

Lefèvre, W. (edit.). (2007). Inside the Camera Obscura –Optics and Art under the Spell of the Projected Image. Berlin: Max-Planck-Intitut für Wissenschafts Geschichte.

Lindberg, D. (1970). A reconsideration of Roger Bacon’s Theory of Pinhole Images. Archive for History of Exact Sciences, vol. 6, No. 3, pp. 214-223.

Lohne, J. (1968). Der eigenartige Einfluβ Witelos auf die Entwicklung der Dioptrik. Archive for History of Exact Sciences, vol. 4, pp. 414-426.

Malebranche, N. (1712/2009). Acerca de la investigación de la verdad. Salamanca: Ediciones Sígueme.

Malet, A. (1990). Keplerian Illusions: Geometrical Pictures vs Optical Images in Kepler´s Visual Theory. Studies in History and Philosophy of Sciences, vol. 21, No. 1, pp. 1-40.

Noë, A. (2006). Action in Perception. Cambridge (Mass): The MIT Press.

Ptolomeo. (trad. en 1996). Optics. En A. Mark Smith (Edit. y Trad.), Ptolemy’s Theory of Visual Perception (pp. 67-261). Philadelphia: The American Philosophical Society.

Raynaud, D. (2016). A Critical Edition of Ibn al-Haytham’s On the Shape of the Eclipse. Cham: Springer Verlag.

Risner, F. (edit.). (1572). Opticae thesaurus Alhazeni Arabis libri septem… Item Vitellonis Thuringopoloni libri decem. Basile: Per episcopios.

Sabra, A. (2007). Alhazen´s Optics in Europe: Some Notes on What It said and What It Did Not Say. En W. Lefèvre (edit.), pp. 53-57.

Shapiro, A. (2007). Images: Real and Virtual, Projected and Perceived, from Kepler to Dechales. En W. Lefèvre (edit.), 2007, pp. 75-94.

Smith, M. (edit. y trad.). (1996). Ptolemy’s Theory of Visual Perception. Philadelphia: The American Philosophical Society.

Smith, M. (edit. y trad.). (2001). Alhacen’s Theory of visual perception. Philadelphia: American Philosophical Society. Traducción al inglés con comentarios de los tres primeros libros del De Aspectibus de Alhacén, 2 vol.

Straker, S. (1971). Kepler´s Optics: A Study in the Development of Seventeenth Century Philosophy. (Tesis doctoral). Universidad de Indiana, Bloomington.

Published

2021-07-08

Issue

Section

VARIA