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The journey of light: from burning mirrors to LED technology (part I)

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Lettera Matematica

Abstract

This is part I of a two-part investigation of the propagation of light. Here we discuss the propagation of wave in materials with constant refractive index, that is, homogeneous media. Its mathematical modelling, known as geometric optics, places an essential role in interpreting reflection, refraction and total internal reflection. Here we begin with the speculations of Hero and going to those of Descartes and Fermat. In part II we will introduce a general and abstract model of optimisation encompassing both space and time geodesics. Based on Newton’s calculus, it allows us to treat a number of phenomena well beyond geometric optics.

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Notes

  1. Catroptics is sometimes attributed to a later author.

  2. Actually the trajectories are local extrema (local stationary points), in the sense that the length is minimal or maximal only with respect to ‘nearby’ trajectories.

  3. Alhazen’s works were probably translated into Latin during the 12th c. AD.

  4. Probably of Polish descent, even the name is uncertain. He may have spent a long time in Italy, studying in Padua (1262–1268) and Viterbo.

  5. The fresco by Thomas of Modena is the church of S. Niccolò in Treviso. The monk depicted is Friar Ugone of Provence.

  6. The first Keplerian telescope was built by C. Scheiner in 1630.

  7. Galileo, informed about the invention of a Dutch craftsman, had built a telescope by himself.

  8. A wooden stick plunged in a glass of water will appear to be broken at the point where it enters the water.

  9. Descartes’s key idea is based on the decomposition of the velocity of light, an idea he got from Alhazen. For this reason the discovery of the law should be attributed to the Arab scientist instead.

  10. Analysis ad refractiones, letter dated January 1, 1662 and addressed to De La Chambre.

  11. The (absolute) refraction index of a homogeneous, isotropic medium is the ratio between the speed of light in vacuum (c = 3 × 108 m/s) and the speed in the medium. The latter obviously depends on the physical properties and characteristics of the medium.

  12. To be precise, the trajectories are local extrema or local stationary points for time, in the sense that the duration is minimal with respect to ‘nearby’ trajectories.

  13. The point is called Fermat point.

References

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  5. Manara, C. F. Sul problema detto di Alhazen. L’insegnamento della Matematica e delle Scienze Integrate 2 (1999). http://www.carlofelicemanara.it/public/file/File/Divulgazione/Collaborazioni%20a%20riviste/Periodico%20IMSI/Sul%20problema%20di%20Alhazen-IMSI.pdf

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, 06123, Perugia, Italy

    Primo Brandi & Anna Salvadori

Authors
  1. Primo Brandi
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  2. Anna Salvadori
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Correspondence to Primo Brandi or Anna Salvadori.

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As co-authors Primo Brandi and Anna Salvadori have published numerous works, including Prima di iniziare. Conoscenze e competenze matematiche di base per l’università (Perugia, Aguaplano, 2011) and Modelli Matematici Elementari (Milan, Bruno Mondadori, 2004).

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Brandi, P., Salvadori, A. The journey of light: from burning mirrors to LED technology (part I). Lett Mat Int 3, 221–234 (2015). https://doi.org/10.1007/s40329-015-0103-3

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