Skip to main content
SpringerLink
Log in

A short history of the rainbow

  • Published:
Lettera Matematica

Abstract

The history of the rainbow is as old as that of science. The ancient Greek philosophers tried to describe the rainbow, and Aristotle was the first to fully include it among the phenomena studied by physicists. Sunlight reflected in the clouds, the incidence of light rays, the reason for the rainbow’s circular shape, the optical effect of an infinite depth are aspects that have for centuries intrigued scholars, who studied the rainbow with a mixture science and alchemy, sense and sensibility. In the 17th century the rainbow became a strictly physical phenomenon, the object of rigorous investigations according to the law of reflection and refraction. Here we survey this often forgotten history, from ancient Greeks to modern scientists, the rainbow’s colours belonging to the world of physics but also—as Thomas Young wrote in 1803—to the world of speculation and imagination.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  1. In his treatise De iride et de radialibus impressionibus, Theodoric provided a first scientific explanation, still considered phenomenologically valid, of the rainbow, a phenomenon that had already attracted the interest of such scholars as Robert Grosseteste (ca. 1175–1253), Roger Bacon and Witelo (Erazmus Ciolek Witelo, also known as Vitellio, (ca. 1230-post 1280/ante 1314). The German Dominican gave an interpretation of the rainbow as a result of refraction of light in its spectrum of colours, even though he was not actually a scientist, nor in particular an experimentalist, and as a consequence he did not master the experimental method; nevertheless, he showed an attitude to research with a properly scientific object. So the German scholar is a natural interpreter of studies “in the tradition of Albertus Magnus” [see Elisa Chiti, article “Teodorico di Freiberg” in online Manuale di Filosofia Medievale published by the University of Siena, Faculty of Letters and Philosophy]. As regards Theodoric’s work, see his Opera Omnia [44]; it includes the writings De coloribus, De elementis corporum naturalium, De iride et de radialibus impressionibus, De luce et eius origine, De miscibilibus in mixto, De tempore. See also Venturi [45], part III: “Dell’Iride”, pp. 149–246 and Krebs [30].

  2. See, in this regard, Corradi [14].

  3. Kamāl al-Dīn Hasan ibn Ali ibn Hasan al-Fārisī, or Abu Hasan Muhammad ibn Hasan, a mathematician born in Tabriz (Iran), gave important contributions to number theory and to the mathematical theory of light, with interesting insights about colours and rainbows (see Roshdi Rashed, s.v. al-Fārisī, in [48]).

  4. See Gazi Topdemir [23].

  5. See Boyer [7].

  6. See Boyer [8], pp. 127–129.

  7. See Sivin [43], p. 24.

  8. See Albertus Magnus [2], Meteora, Liber III, Meteororum, Trac. IV, Caput X “De causa efficiente et materiali colorum iridis in communi”, pp. 678–679.

  9. See Hackett [27].

  10. See vol. II, pp. 172–201 of Bridges [12]. Moreover, it is necessary to remark that, at the end of 13th century, the Polish philosopher and physicist Witelo, building on Alhazen’s hypoteses, had claimed that the bending of light by refraction was larger the denser the medium through which light had passed. Witelo’s essay, Vitellonis Thuringopoloni opticæ libri decem, is contained in Opticæ Thesaurus by Friedrich Risner (1533-1580), published in Basel in 1572. See also El-Bizri [20].

  11. The writings appearing in this treatise were composed between 1521 and 1552.

  12. See Gedselman [24].

  13. Snell’s law, also known as Snell-Descartes law, describes how a light ray is refracted when passing from a medium to another one with a different refractive index; in general, it is valid only for isotropic substances, such as glass, and shows several similarities to Fermat’s principle (due to Pierre de Fermat, 1601–1665) that “the path taken between two points by a ray of light is the path that can be traversed in the least time”. A first formulation of Snell-Descartes law can be found in a manuscript by the Arab mathematician Abū Sa’d al-‘Alā’ ibn Sahl (X sec.) written in 984; it was later probably guessed in 1602 by Thomas Harriot (1560–1621), an astronomer and a mathematician, who did not publish his work, though. It was rediscovered by Willebrord Snell in 1621, in a form mathematically equivalent, unpublished until his death, and, phinally, republished by Descartes in terms of sine functions in his 1637 Discours de la méthode…, where he used it to solve several problems in optics.

  14. See Brand [10], pp. 30–32.

  15. See Crew [15] and Kipnis [29].

  16. See Berlin-Kay [4].

  17. “Ex quo clarissime apparet, lumina variorum colorum varia esset refrangibilitate: idque eo ordine, ut color ruber omnium minime refrangibilis sit, reliqui autem colores, aureus, flavus, viridis, cæruleus, indicus, violaceus, gradatim and ex ordine magis magisque refrangibiles”, Newton [40], Propositio II, Experimentum VII.

  18. See Gage [22], p. 140.

  19. “When a ray of light is polarised by reflexion, the reflected ray forms a right angle with the refracted ray”, Brewster [11], p. 132.

  20. See for instance Venturi [45], Mascart [36], Minnaert-Lynch-Livingston [38], Nussenzveig [41], Greenler [26], Boyer [9], Blay [6], Lynch-Livingston [33], Lee-Fraser [31], Maitte [34].

  21. For further reading about the controversy Goethe-Newton about colours, see [14].

  22. From Goethe's Maximen und Reflexionen.

  23. For the last two quotations, see [1], p.86.

References

  1. Ainger, A.: Charles Lamb. Cambridge University, Cambridge (2011)

    Book  Google Scholar 

  2. Albertus Magnus: Opera omnia. In: Borgnet, A. (ed.). Vivès, Paris (1890)

  3. Asimov, I.: Eyes on the Universe: a history of the telescope. H. Mifflin, Boston (1975)

    Google Scholar 

  4. Berlin, B., Kay, P.: Basic color terms: their Universality and evolution. University of California, Berkeley (1969)

    Google Scholar 

  5. Biddell Airy, G.: On the intensity of light in the neighbourhood of a caustic. Trans. Camb. Philos. Soc. 6, 379–402 (1838)

    Google Scholar 

  6. Blay, M.(ed.): Les figures de l’arc-en-ciel. Carré, Paris (1995)

  7. Boyer, C.B.: Robert grosseteste on the rainbow. Osiris 11, 247–258 (1954)

    Article  Google Scholar 

  8. Boyer, C.B.: The rainbow: from myth to mathematics. Yoseloff, New York (1959)

    Google Scholar 

  9. Boyer, C.B.: The rainbow, from myth to mathematics. Princeton University, Princeton (1987)

    Google Scholar 

  10. Brand, J.: Lines of light: the sources of dispersive spectroscopy, 1800–1930. CRC Press, Boca Raton (1995)

    Google Scholar 

  11. Brewster, D.: On the laws which regulate the polarisation of light by reflection from transparent bodies. Philos. Trans. R. Soc. Lond. 105, 125–159 (1815)

    Article  Google Scholar 

  12. Bridges, J.H.: The opus majus of Roger Bacon, vol. I & II. Williams and Norgate, London (1900)

    Google Scholar 

  13. Byron, G.G.: The bride of Abydos: a Turkish tale. J. Murray, London (1813)

    Google Scholar 

  14. Corradi, M.: La teoria dei colori di Johann Wolfgang von Goethe. In: Rossi, M., Marchiafava, V. (eds.) Colore e colorimetria. Contributi multidisciplinari, Vol. X A, pp. 401–712. Maggioli, S. Arcangelo di Romagna (2014)

  15. Crew, H.: The wave theory of light; memoirs of Huygens, Young and Fresnel. American Book Company, New York (1900)

    Google Scholar 

  16. Crombie, A.C.: Robert grosseteste and the origins of experimental science. Clarendon Press, Oxford (1983)

    Google Scholar 

  17. De Dominis, M.A.: De radiis visus et lucis in vitris perspectivis et iride tractatus Marci Antonii de Dominis, Per Ioannem Bartolum in lucem editus: in quo inter alia ostenditur ratio instrumenti cuiusdam ad clare videndum, quae sunt valde remota excogitati. Thoma Baglionus, Venice (1611)

  18. Descartes, R.: Discours de la méthode pour bien conduire sa raison, et chercher la verité dans les sciences Plus la Dioptrique, les Meteores, et la Geometrie qui sont des essais de cete Methode. Ian Maire, Leyde (1637)

  19. Descartes, R.: The World and Other Writings (English translation by Gaukroger, S.). Cambridge University, Cambridge (2004)

  20. El-Bizri, N.: A philosophical perspective on Alhazen’s optics. Arab. Sci. Philos. 15, 189–218 (2005)

    Article  Google Scholar 

  21. Fleischer, J.: De iridibus doctrina Aristotelis et Vitellionis. Iohannes Crato, Wittenberg (1571)

  22. Gage, J.: Color and meaning. art, science and symbolism. University of California, Berkeley (1994)

    Google Scholar 

  23. GaziTopdemir, H.: Kamal Al-Din Al-Farisi’s explanation of the rainbow. Humanit Soc Sci J 2, 75–85 (2007)

    Google Scholar 

  24. Gedselman, S.D.: Did Kepler’s Supplement to ‘Witelo’ Inspire Descartes’ Theory on the Rainbow? Bulletin American Meteorological Society 70, 750–751 (1989)

    Article  Google Scholar 

  25. Goethe, J.W.: Zur Farbenlehre. J.G. Cotta’schen Buchhandlung, Tübingen (1810)

    Google Scholar 

  26. Greenler, R.: Rainbows, Halos, and Glories. Cambridge University, Cambridge (1980)

    Google Scholar 

  27. Hackett, J.: Experientia, Experimentum and Perception of Objects in Space: Roger Bacon. In: Aertsen, J.A., Speer, A. (eds.) Raum und Raumvorstellungen im Mittelalter, pp. 101–120. Walter de Gruyter, Berlin (1998)

  28. Khare, V., Nussenzveig, H.M.: Theory of the rainbow. Phys. Rev. Lett. 33, 976–980 (1974)

    Article  Google Scholar 

  29. Kipnis, N.: History of the principle of interference of light. Birkhäuser, Berlin (1990)

    Google Scholar 

  30. Krebs, E.: Meister Dietrich (Theodoricus Teutonicus de Vriberg) sein Leben, seine Werke, seine Wissenschaft. In: Beiträge zur Geschichte der Philosophie des Mittelalters, Texte u. Untersuchungen, part V, pp. 5–6. Aschendorff, Münster (1906)

  31. Lee, R.L., Fraser, A.B.: The rainbow bridge: rainbows in art, myth, and science. Penn State Press, University Park (2001)

    Google Scholar 

  32. Lindberg, D.C.: Roger Bacon’s theory of the rainbow: progress or regress? Isis 57, 235 (1966)

    Article  Google Scholar 

  33. Lynch, D.K., Livingston, W.: Color and Light in Nature, 2nd edn. Cambridge University, Cambridge (2001)

    Google Scholar 

  34. Maitte, B.: Histoire de l’arc-en-ciel. Seuil, Paris (2005)

    Google Scholar 

  35. Mariotte, E.: Essais de physique, ou Mémoires pour servir à la science des choses naturelles. Michallet, Paris (1679–81)

  36. Mascart, É.: Traité d’Optique, 3 voll. Gauthier-Villars, Paris (1894)

    Google Scholar 

  37. Maurolico, F.: Photismi de lumine et umbra ad perspectivam, and radiorum incidentiam facientes. Diaphanorum partes, seu libri tres. Editio princeps. Tarquinius Longus, Naples (1611)

  38. Minnaert, M.G.J., Lynch, D.K., Livingston, W.: The nature of light and color in the open air. Dover Publications, New York (1973)

    Google Scholar 

  39. Newton, I.: Opticks or, a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light: also Two Treatises of the Species and Magnitude of Curvilinear Figures. Sam. Smith and Benj. Walford, London (1704)

  40. Newton, I.: Optice: Sive de Reflexionibus, Refractionibus, Inflexionibus and Coloribus Lucis Libri Tres. Marci-Michaelis Bousquet, Lausanne/Geneva (1740)

  41. Nussenzveig, H.M.: The theory of the rainbow. Sci. Am. 236, 116–127 (1977)

    Article  Google Scholar 

  42. Potter, R.: Mathematical considerations on the prohlem of the rainbow, shewing it to belong to physical optics. Trans. Camb. Philos. Soc. 6, 141–152 (1838)

    Google Scholar 

  43. Sivin, N.: Science in ancient China: researches and reflections. Ashgate Publishing, Brookfield, Vermont (1995)

    Google Scholar 

  44. Theodoricus de Vriberg: Opera Omnia, voll. I-IV. In: Cavigioli, J.-D., Imbach, R., Mojsisch, B., Pagnoni-Sturlese, M. R., Rehn, R., Steffan, H., Sturlese, L., Wallace, W. A. (eds.) Corpus Philosophorum Teutonicorum Medii Aevi II/1-4, Meiner, Hamburg (1994)

  45. Venturi, G.B.: Commentari sopra la storia e le teorie dell’ottica. I. Masi, Bologna (1814)

    Google Scholar 

  46. Young, T.: The Bakerian Lecture: on the theory of light and colours. Philos. Trans. R. Soc. Lond. 92, 12–48 (1802)

    Article  Google Scholar 

  47. Young, T.: The Bakerian Lecture: experiments and calculations relative to physical optics. Philos. Trans. R. Soc. 94, 1–16 (1804)

    Article  Google Scholar 

  48. Dictionary of scientific biography. American Council of Learned Societies, Charles Scribner’s Sons, New York (1970–1990)

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Scienze per l’Architettura, Scuola Politecnica, Università degli Studi di Genova, Stradone di Sant’Agostino 37, 16121, Genoa, Italy

    Massimo Corradi

Authors
  1. Massimo Corradi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Massimo Corradi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Corradi, M. A short history of the rainbow. Lett Mat Int 4, 49–57 (2016). https://doi.org/10.1007/s40329-016-0127-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40329-016-0127-3

Keywords

Search

Navigation