Abstract

We present a new analysis of Robert Grosseteste’s account of color in his treatise De iride (On the Rainbow), dating from the early 13th century. The work explores color within the 3D framework set out in Grosseteste’s De colore [see J. Opt. Soc. Am. A 29, A346 (2012)], but now links the axes of variation to observable properties of rainbows. We combine a modern understanding of the physics of rainbows and of human color perception to resolve the linguistic ambiguities of the medieval text and to interpret Grosseteste’s key terms.

© 2014 Optical Society of America

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  1. Our dating is based on C. Panti, “Robert Grosseteste and Adam of Exeter’s physics of light, remarks on the transmission, authenticity and chronology of Grosseteste’s scientific opuscula,” in Robert Grosseteste and His Intellectual Milieu, J. Flood, J. Ginther, and J. Goering, eds. (Toronto, 2013), 165–190 at p. 185, Table 1, “A Tentative Chronology of Grosseteste’s Scientific Works.” Most commentators agree on the later dating, but not on the specific date-range: A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100–1700 (Oxford, 1953), p. 51: 1230–1235; R. W. Southern, Robert Grosseteste: The Growth of an English Mind in Medieval Europe, 2nd ed. (Oxford, 1992), p. 120: 1230–1233; R. C. Dales, “Robert Grosseteste’s Scientific Works,” Isis 52, 381–402, (1961) at 402: 1232–1235; J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983), at 655: 1230–1233.
  2. H. E. Smithson, G. Dinkova-Bruun, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, and C. Panti, “A three-dimensional color space from the 13th century,” J. Opt. Soc. Am. A 29, A346–A352 (2012).
    [CrossRef]
  3. L. Baur, Die philosophischen Werke des Robert Grosseteste, Bischofs von Lincoln. Zum erstenmal vollständig in kritischer Ausgabe (Aschendorf, Münster, 1912).
  4. D. C. Lindberg, “On the rainbow,” in A Source Book in Medieval Science, E. Grant, ed. (Harvard, 1974), pp. 388–391.
  5. A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science 1100–1700 (Oxford University, 1953).
  6. B. S. Eastwood, “Robert Grosseteste’s theory of the rainbow: a chapter in the history of non-experimental science,” Arch. Int. Hist. Sci. 19, 313–332 (1966).
  7. C. B. Boyer, “Robert Grosseteste on the rainbow,” Osiris 11, 247–258 (1954).
    [CrossRef]
  8. D. C. Lindberg, “Roger Bacon’s theory of the rainbow: progress or regress?” Isis 57, 235–248 (1966).
    [CrossRef]
  9. R. C. Dales, “Robert Grosseteste’s scientific works,” Isis 52, 381–402 (1961).
    [CrossRef]
  10. J. J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983).
    [CrossRef]
  11. P. S. Anderson, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, H. E. Smithson, S. Sonnesyn, and B. K. Tanner, The Refraction of Rays: Robert Grosseteste’s De iride, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, Toronto (to be published).
  12. G. Dinkova-Brunn, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, and H. E. Smithson, The Dimensions of Colour: Robert Grosseteste’s De colore, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, 2013).
  13. J. J. Koenderink, Color for the Sciences (MIT, 2010).
  14. Grosseteste uses here the Latin term lumen, not lux as he did in the De colore. Throughout his writings, Grossteste is careful to distinguish between source or essence of light (lux), and reflected light (lumen). To be faithful to this distinction, and to highlight to the modern reader that such a distinction exists in the Latin, we translate lumen here as “luminosity,” not “light.” However, our use of the word “luminosity” in this context should not be confused with the technical use of the term in modern vision science.
  15. Similarly, he uses here admixtum cum, not incorporatum as he did in the De colore, which we translate as “mixed with,” not “embodied in.”
  16. Grosseteste uses here the Latin adjective hyazinthinus, from the substantive hyacinthus, which we choose to translate as purple. The sources here are complex and are based on medieval references to gem stones and other color terminology. So, the identification with any particular color is blurred, but on-balance we believe that violet or purple with some red is an appropriate interpretation. The fact that in the (perceptual) hue circle (but not on a wavelength scale) violet, purple and red are adjacent is also worth noting.
  17. R. Descartes, Discourse on Method, Optics, Geometry and Metereology, trans. P. J. Olscamp, ed., rev. (Hackett, 2001, orig. publ. 1965) Metereology, Eighth Discourse, pp. 332–345.
  18. C. B. Boyer, The Rainbow: From Myth to Mathematics (Yoseloff, 1959).
  19. J. D. Mollon, “The origins of modern color science,” in Color Science, S. Shevell, ed. (Optical Society of America, 2003).
  20. G. B. Airy, “On the intensity of light in the neighbourhood of a caustic,” Trans. Cambridge Philos. Soc. 6, Part 3, 397–403 (1838).
  21. E. A. Hovenac and J. A. Lock, “Assessing the contributions of surface waves and complex rays to far-field Mie scattering by use of the Debye series,” J. Opt. Soc. Am. A 9, 781–795 (1992).
    [CrossRef]
  22. P. Laven, “Simulation of rainbows, coronas, and glories by use of Mie theory,” Appl. Opt. 42, 436–444 (2003).
    [CrossRef]
  23. P. Laven, “Simulation of rainbows, coronas and glories using Mie theory and the Debye series,” J. Quant. Spectrosc. Radiat. Transfer 89, 257–269 (2004).
    [CrossRef]
  24. R. L. Lee, “Mie theory, Airy theory, and the natural rainbow,” Appl. Opt. 37, 1506–1519 (1998).
    [CrossRef]
  25. The dominant wavelength of a particular spectral distribution is formally defined as the wavelength of monochromatic light that when added to a reference white light would produce a perceptual color match to the spectrum in question. A change in dominant wavelength is generally associated with a change in hue.
  26. F. Kasten and A. T. Young, “Revised optical air-mass tables and approximation formula,” Appl. Opt. 28, 4735–4738 (1989).
    [CrossRef]
  27. C. W. Allen, Astrophysical Quantities (Athlone, 1973).
  28. K. Bogumil, J. Orphal, J. P. Burrows, and J. M. Flaud, “Vibrational progressions in the visible and near-ultraviolet absorption spectrum of ozone,” Chem. Phys. Lett. 349, 241–248 (2001).
    [CrossRef]
  29. R. L. Lee, “What are all the colors of the rainbow,” Appl. Opt. 30, 3401–3407 (1991).
    [CrossRef]
  30. D. I. A. Macleod and R. M. Boynton, “Chromaticity diagram showing cone excitation by stimuli of equal luminance,” J. Opt. Soc. Am. 69, 1183–1186 (1979).
    [CrossRef]
  31. I. Sadeghi, A. Munoz, P. Laven, W. Jarosz, F. Seron, D. Gutierrez, and H. W. Jensen, “Physically based simulation of rainbows,” ACM Trans. Graph. 31, 3 (2012).
    [CrossRef]

2013 (1)

Our dating is based on C. Panti, “Robert Grosseteste and Adam of Exeter’s physics of light, remarks on the transmission, authenticity and chronology of Grosseteste’s scientific opuscula,” in Robert Grosseteste and His Intellectual Milieu, J. Flood, J. Ginther, and J. Goering, eds. (Toronto, 2013), 165–190 at p. 185, Table 1, “A Tentative Chronology of Grosseteste’s Scientific Works.” Most commentators agree on the later dating, but not on the specific date-range: A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100–1700 (Oxford, 1953), p. 51: 1230–1235; R. W. Southern, Robert Grosseteste: The Growth of an English Mind in Medieval Europe, 2nd ed. (Oxford, 1992), p. 120: 1230–1233; R. C. Dales, “Robert Grosseteste’s Scientific Works,” Isis 52, 381–402, (1961) at 402: 1232–1235; J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983), at 655: 1230–1233.

Our dating is based on C. Panti, “Robert Grosseteste and Adam of Exeter’s physics of light, remarks on the transmission, authenticity and chronology of Grosseteste’s scientific opuscula,” in Robert Grosseteste and His Intellectual Milieu, J. Flood, J. Ginther, and J. Goering, eds. (Toronto, 2013), 165–190 at p. 185, Table 1, “A Tentative Chronology of Grosseteste’s Scientific Works.” Most commentators agree on the later dating, but not on the specific date-range: A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100–1700 (Oxford, 1953), p. 51: 1230–1235; R. W. Southern, Robert Grosseteste: The Growth of an English Mind in Medieval Europe, 2nd ed. (Oxford, 1992), p. 120: 1230–1233; R. C. Dales, “Robert Grosseteste’s Scientific Works,” Isis 52, 381–402, (1961) at 402: 1232–1235; J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983), at 655: 1230–1233.

Our dating is based on C. Panti, “Robert Grosseteste and Adam of Exeter’s physics of light, remarks on the transmission, authenticity and chronology of Grosseteste’s scientific opuscula,” in Robert Grosseteste and His Intellectual Milieu, J. Flood, J. Ginther, and J. Goering, eds. (Toronto, 2013), 165–190 at p. 185, Table 1, “A Tentative Chronology of Grosseteste’s Scientific Works.” Most commentators agree on the later dating, but not on the specific date-range: A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100–1700 (Oxford, 1953), p. 51: 1230–1235; R. W. Southern, Robert Grosseteste: The Growth of an English Mind in Medieval Europe, 2nd ed. (Oxford, 1992), p. 120: 1230–1233; R. C. Dales, “Robert Grosseteste’s Scientific Works,” Isis 52, 381–402, (1961) at 402: 1232–1235; J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983), at 655: 1230–1233.

Our dating is based on C. Panti, “Robert Grosseteste and Adam of Exeter’s physics of light, remarks on the transmission, authenticity and chronology of Grosseteste’s scientific opuscula,” in Robert Grosseteste and His Intellectual Milieu, J. Flood, J. Ginther, and J. Goering, eds. (Toronto, 2013), 165–190 at p. 185, Table 1, “A Tentative Chronology of Grosseteste’s Scientific Works.” Most commentators agree on the later dating, but not on the specific date-range: A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100–1700 (Oxford, 1953), p. 51: 1230–1235; R. W. Southern, Robert Grosseteste: The Growth of an English Mind in Medieval Europe, 2nd ed. (Oxford, 1992), p. 120: 1230–1233; R. C. Dales, “Robert Grosseteste’s Scientific Works,” Isis 52, 381–402, (1961) at 402: 1232–1235; J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983), at 655: 1230–1233.

Our dating is based on C. Panti, “Robert Grosseteste and Adam of Exeter’s physics of light, remarks on the transmission, authenticity and chronology of Grosseteste’s scientific opuscula,” in Robert Grosseteste and His Intellectual Milieu, J. Flood, J. Ginther, and J. Goering, eds. (Toronto, 2013), 165–190 at p. 185, Table 1, “A Tentative Chronology of Grosseteste’s Scientific Works.” Most commentators agree on the later dating, but not on the specific date-range: A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100–1700 (Oxford, 1953), p. 51: 1230–1235; R. W. Southern, Robert Grosseteste: The Growth of an English Mind in Medieval Europe, 2nd ed. (Oxford, 1992), p. 120: 1230–1233; R. C. Dales, “Robert Grosseteste’s Scientific Works,” Isis 52, 381–402, (1961) at 402: 1232–1235; J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983), at 655: 1230–1233.

2012 (2)

H. E. Smithson, G. Dinkova-Bruun, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, and C. Panti, “A three-dimensional color space from the 13th century,” J. Opt. Soc. Am. A 29, A346–A352 (2012).
[CrossRef]

I. Sadeghi, A. Munoz, P. Laven, W. Jarosz, F. Seron, D. Gutierrez, and H. W. Jensen, “Physically based simulation of rainbows,” ACM Trans. Graph. 31, 3 (2012).
[CrossRef]

2004 (1)

P. Laven, “Simulation of rainbows, coronas and glories using Mie theory and the Debye series,” J. Quant. Spectrosc. Radiat. Transfer 89, 257–269 (2004).
[CrossRef]

2003 (1)

2001 (1)

K. Bogumil, J. Orphal, J. P. Burrows, and J. M. Flaud, “Vibrational progressions in the visible and near-ultraviolet absorption spectrum of ozone,” Chem. Phys. Lett. 349, 241–248 (2001).
[CrossRef]

1998 (1)

1992 (1)

1991 (1)

1989 (1)

1983 (1)

J. J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983).
[CrossRef]

1979 (1)

1966 (2)

D. C. Lindberg, “Roger Bacon’s theory of the rainbow: progress or regress?” Isis 57, 235–248 (1966).
[CrossRef]

B. S. Eastwood, “Robert Grosseteste’s theory of the rainbow: a chapter in the history of non-experimental science,” Arch. Int. Hist. Sci. 19, 313–332 (1966).

1961 (1)

R. C. Dales, “Robert Grosseteste’s scientific works,” Isis 52, 381–402 (1961).
[CrossRef]

1954 (1)

C. B. Boyer, “Robert Grosseteste on the rainbow,” Osiris 11, 247–258 (1954).
[CrossRef]

1838 (1)

G. B. Airy, “On the intensity of light in the neighbourhood of a caustic,” Trans. Cambridge Philos. Soc. 6, Part 3, 397–403 (1838).

Airy, G. B.

G. B. Airy, “On the intensity of light in the neighbourhood of a caustic,” Trans. Cambridge Philos. Soc. 6, Part 3, 397–403 (1838).

Allen, C. W.

C. W. Allen, Astrophysical Quantities (Athlone, 1973).

Anderson, P. S.

P. S. Anderson, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, H. E. Smithson, S. Sonnesyn, and B. K. Tanner, The Refraction of Rays: Robert Grosseteste’s De iride, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, Toronto (to be published).

Baur, L.

L. Baur, Die philosophischen Werke des Robert Grosseteste, Bischofs von Lincoln. Zum erstenmal vollständig in kritischer Ausgabe (Aschendorf, Münster, 1912).

Bogumil, K.

K. Bogumil, J. Orphal, J. P. Burrows, and J. M. Flaud, “Vibrational progressions in the visible and near-ultraviolet absorption spectrum of ozone,” Chem. Phys. Lett. 349, 241–248 (2001).
[CrossRef]

Boyer, C. B.

C. B. Boyer, “Robert Grosseteste on the rainbow,” Osiris 11, 247–258 (1954).
[CrossRef]

C. B. Boyer, The Rainbow: From Myth to Mathematics (Yoseloff, 1959).

Boynton, R. M.

Burrows, J. P.

K. Bogumil, J. Orphal, J. P. Burrows, and J. M. Flaud, “Vibrational progressions in the visible and near-ultraviolet absorption spectrum of ozone,” Chem. Phys. Lett. 349, 241–248 (2001).
[CrossRef]

Crombie, A. C.

Our dating is based on C. Panti, “Robert Grosseteste and Adam of Exeter’s physics of light, remarks on the transmission, authenticity and chronology of Grosseteste’s scientific opuscula,” in Robert Grosseteste and His Intellectual Milieu, J. Flood, J. Ginther, and J. Goering, eds. (Toronto, 2013), 165–190 at p. 185, Table 1, “A Tentative Chronology of Grosseteste’s Scientific Works.” Most commentators agree on the later dating, but not on the specific date-range: A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100–1700 (Oxford, 1953), p. 51: 1230–1235; R. W. Southern, Robert Grosseteste: The Growth of an English Mind in Medieval Europe, 2nd ed. (Oxford, 1992), p. 120: 1230–1233; R. C. Dales, “Robert Grosseteste’s Scientific Works,” Isis 52, 381–402, (1961) at 402: 1232–1235; J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983), at 655: 1230–1233.

A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science 1100–1700 (Oxford University, 1953).

Dales, R. C.

Our dating is based on C. Panti, “Robert Grosseteste and Adam of Exeter’s physics of light, remarks on the transmission, authenticity and chronology of Grosseteste’s scientific opuscula,” in Robert Grosseteste and His Intellectual Milieu, J. Flood, J. Ginther, and J. Goering, eds. (Toronto, 2013), 165–190 at p. 185, Table 1, “A Tentative Chronology of Grosseteste’s Scientific Works.” Most commentators agree on the later dating, but not on the specific date-range: A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100–1700 (Oxford, 1953), p. 51: 1230–1235; R. W. Southern, Robert Grosseteste: The Growth of an English Mind in Medieval Europe, 2nd ed. (Oxford, 1992), p. 120: 1230–1233; R. C. Dales, “Robert Grosseteste’s Scientific Works,” Isis 52, 381–402, (1961) at 402: 1232–1235; J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983), at 655: 1230–1233.

R. C. Dales, “Robert Grosseteste’s scientific works,” Isis 52, 381–402 (1961).
[CrossRef]

Descartes, R.

R. Descartes, Discourse on Method, Optics, Geometry and Metereology, trans. P. J. Olscamp, ed., rev. (Hackett, 2001, orig. publ. 1965) Metereology, Eighth Discourse, pp. 332–345.

Dinkova-Brunn, G.

G. Dinkova-Brunn, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, and H. E. Smithson, The Dimensions of Colour: Robert Grosseteste’s De colore, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, 2013).

Dinkova-Bruun, G.

Eastwood, B. S.

B. S. Eastwood, “Robert Grosseteste’s theory of the rainbow: a chapter in the history of non-experimental science,” Arch. Int. Hist. Sci. 19, 313–332 (1966).

Flaud, J. M.

K. Bogumil, J. Orphal, J. P. Burrows, and J. M. Flaud, “Vibrational progressions in the visible and near-ultraviolet absorption spectrum of ozone,” Chem. Phys. Lett. 349, 241–248 (2001).
[CrossRef]

Gasper, G. E. M.

H. E. Smithson, G. Dinkova-Bruun, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, and C. Panti, “A three-dimensional color space from the 13th century,” J. Opt. Soc. Am. A 29, A346–A352 (2012).
[CrossRef]

G. Dinkova-Brunn, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, and H. E. Smithson, The Dimensions of Colour: Robert Grosseteste’s De colore, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, 2013).

P. S. Anderson, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, H. E. Smithson, S. Sonnesyn, and B. K. Tanner, The Refraction of Rays: Robert Grosseteste’s De iride, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, Toronto (to be published).

Gutierrez, D.

I. Sadeghi, A. Munoz, P. Laven, W. Jarosz, F. Seron, D. Gutierrez, and H. W. Jensen, “Physically based simulation of rainbows,” ACM Trans. Graph. 31, 3 (2012).
[CrossRef]

Hovenac, E. A.

Huxtable, M.

H. E. Smithson, G. Dinkova-Bruun, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, and C. Panti, “A three-dimensional color space from the 13th century,” J. Opt. Soc. Am. A 29, A346–A352 (2012).
[CrossRef]

P. S. Anderson, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, H. E. Smithson, S. Sonnesyn, and B. K. Tanner, The Refraction of Rays: Robert Grosseteste’s De iride, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, Toronto (to be published).

G. Dinkova-Brunn, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, and H. E. Smithson, The Dimensions of Colour: Robert Grosseteste’s De colore, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, 2013).

Jarosz, W.

I. Sadeghi, A. Munoz, P. Laven, W. Jarosz, F. Seron, D. Gutierrez, and H. W. Jensen, “Physically based simulation of rainbows,” ACM Trans. Graph. 31, 3 (2012).
[CrossRef]

Jensen, H. W.

I. Sadeghi, A. Munoz, P. Laven, W. Jarosz, F. Seron, D. Gutierrez, and H. W. Jensen, “Physically based simulation of rainbows,” ACM Trans. Graph. 31, 3 (2012).
[CrossRef]

Kasten, F.

Koenderink, J. J.

J. J. Koenderink, Color for the Sciences (MIT, 2010).

Laven, P.

I. Sadeghi, A. Munoz, P. Laven, W. Jarosz, F. Seron, D. Gutierrez, and H. W. Jensen, “Physically based simulation of rainbows,” ACM Trans. Graph. 31, 3 (2012).
[CrossRef]

P. Laven, “Simulation of rainbows, coronas and glories using Mie theory and the Debye series,” J. Quant. Spectrosc. Radiat. Transfer 89, 257–269 (2004).
[CrossRef]

P. Laven, “Simulation of rainbows, coronas, and glories by use of Mie theory,” Appl. Opt. 42, 436–444 (2003).
[CrossRef]

Lee, R. L.

Lindberg, D. C.

D. C. Lindberg, “Roger Bacon’s theory of the rainbow: progress or regress?” Isis 57, 235–248 (1966).
[CrossRef]

D. C. Lindberg, “On the rainbow,” in A Source Book in Medieval Science, E. Grant, ed. (Harvard, 1974), pp. 388–391.

Lock, J. A.

Macleod, D. I. A.

McEvoy, J.

Our dating is based on C. Panti, “Robert Grosseteste and Adam of Exeter’s physics of light, remarks on the transmission, authenticity and chronology of Grosseteste’s scientific opuscula,” in Robert Grosseteste and His Intellectual Milieu, J. Flood, J. Ginther, and J. Goering, eds. (Toronto, 2013), 165–190 at p. 185, Table 1, “A Tentative Chronology of Grosseteste’s Scientific Works.” Most commentators agree on the later dating, but not on the specific date-range: A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100–1700 (Oxford, 1953), p. 51: 1230–1235; R. W. Southern, Robert Grosseteste: The Growth of an English Mind in Medieval Europe, 2nd ed. (Oxford, 1992), p. 120: 1230–1233; R. C. Dales, “Robert Grosseteste’s Scientific Works,” Isis 52, 381–402, (1961) at 402: 1232–1235; J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983), at 655: 1230–1233.

McEvoy, J. J.

J. J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983).
[CrossRef]

McLeish, T. C. B.

H. E. Smithson, G. Dinkova-Bruun, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, and C. Panti, “A three-dimensional color space from the 13th century,” J. Opt. Soc. Am. A 29, A346–A352 (2012).
[CrossRef]

G. Dinkova-Brunn, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, and H. E. Smithson, The Dimensions of Colour: Robert Grosseteste’s De colore, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, 2013).

P. S. Anderson, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, H. E. Smithson, S. Sonnesyn, and B. K. Tanner, The Refraction of Rays: Robert Grosseteste’s De iride, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, Toronto (to be published).

Mollon, J. D.

J. D. Mollon, “The origins of modern color science,” in Color Science, S. Shevell, ed. (Optical Society of America, 2003).

Munoz, A.

I. Sadeghi, A. Munoz, P. Laven, W. Jarosz, F. Seron, D. Gutierrez, and H. W. Jensen, “Physically based simulation of rainbows,” ACM Trans. Graph. 31, 3 (2012).
[CrossRef]

Orphal, J.

K. Bogumil, J. Orphal, J. P. Burrows, and J. M. Flaud, “Vibrational progressions in the visible and near-ultraviolet absorption spectrum of ozone,” Chem. Phys. Lett. 349, 241–248 (2001).
[CrossRef]

Panti, C.

Our dating is based on C. Panti, “Robert Grosseteste and Adam of Exeter’s physics of light, remarks on the transmission, authenticity and chronology of Grosseteste’s scientific opuscula,” in Robert Grosseteste and His Intellectual Milieu, J. Flood, J. Ginther, and J. Goering, eds. (Toronto, 2013), 165–190 at p. 185, Table 1, “A Tentative Chronology of Grosseteste’s Scientific Works.” Most commentators agree on the later dating, but not on the specific date-range: A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100–1700 (Oxford, 1953), p. 51: 1230–1235; R. W. Southern, Robert Grosseteste: The Growth of an English Mind in Medieval Europe, 2nd ed. (Oxford, 1992), p. 120: 1230–1233; R. C. Dales, “Robert Grosseteste’s Scientific Works,” Isis 52, 381–402, (1961) at 402: 1232–1235; J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983), at 655: 1230–1233.

H. E. Smithson, G. Dinkova-Bruun, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, and C. Panti, “A three-dimensional color space from the 13th century,” J. Opt. Soc. Am. A 29, A346–A352 (2012).
[CrossRef]

G. Dinkova-Brunn, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, and H. E. Smithson, The Dimensions of Colour: Robert Grosseteste’s De colore, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, 2013).

P. S. Anderson, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, H. E. Smithson, S. Sonnesyn, and B. K. Tanner, The Refraction of Rays: Robert Grosseteste’s De iride, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, Toronto (to be published).

Sadeghi, I.

I. Sadeghi, A. Munoz, P. Laven, W. Jarosz, F. Seron, D. Gutierrez, and H. W. Jensen, “Physically based simulation of rainbows,” ACM Trans. Graph. 31, 3 (2012).
[CrossRef]

Seron, F.

I. Sadeghi, A. Munoz, P. Laven, W. Jarosz, F. Seron, D. Gutierrez, and H. W. Jensen, “Physically based simulation of rainbows,” ACM Trans. Graph. 31, 3 (2012).
[CrossRef]

Smithson, H. E.

H. E. Smithson, G. Dinkova-Bruun, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, and C. Panti, “A three-dimensional color space from the 13th century,” J. Opt. Soc. Am. A 29, A346–A352 (2012).
[CrossRef]

P. S. Anderson, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, H. E. Smithson, S. Sonnesyn, and B. K. Tanner, The Refraction of Rays: Robert Grosseteste’s De iride, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, Toronto (to be published).

G. Dinkova-Brunn, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, and H. E. Smithson, The Dimensions of Colour: Robert Grosseteste’s De colore, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, 2013).

Sonnesyn, S.

P. S. Anderson, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, H. E. Smithson, S. Sonnesyn, and B. K. Tanner, The Refraction of Rays: Robert Grosseteste’s De iride, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, Toronto (to be published).

Southern, R. W.

Our dating is based on C. Panti, “Robert Grosseteste and Adam of Exeter’s physics of light, remarks on the transmission, authenticity and chronology of Grosseteste’s scientific opuscula,” in Robert Grosseteste and His Intellectual Milieu, J. Flood, J. Ginther, and J. Goering, eds. (Toronto, 2013), 165–190 at p. 185, Table 1, “A Tentative Chronology of Grosseteste’s Scientific Works.” Most commentators agree on the later dating, but not on the specific date-range: A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100–1700 (Oxford, 1953), p. 51: 1230–1235; R. W. Southern, Robert Grosseteste: The Growth of an English Mind in Medieval Europe, 2nd ed. (Oxford, 1992), p. 120: 1230–1233; R. C. Dales, “Robert Grosseteste’s Scientific Works,” Isis 52, 381–402, (1961) at 402: 1232–1235; J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983), at 655: 1230–1233.

Tanner, B. K.

P. S. Anderson, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, H. E. Smithson, S. Sonnesyn, and B. K. Tanner, The Refraction of Rays: Robert Grosseteste’s De iride, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, Toronto (to be published).

Young, A. T.

ACM Trans. Graph. (1)

I. Sadeghi, A. Munoz, P. Laven, W. Jarosz, F. Seron, D. Gutierrez, and H. W. Jensen, “Physically based simulation of rainbows,” ACM Trans. Graph. 31, 3 (2012).
[CrossRef]

Appl. Opt. (4)

Arch. Int. Hist. Sci. (1)

B. S. Eastwood, “Robert Grosseteste’s theory of the rainbow: a chapter in the history of non-experimental science,” Arch. Int. Hist. Sci. 19, 313–332 (1966).

Chem. Phys. Lett. (1)

K. Bogumil, J. Orphal, J. P. Burrows, and J. M. Flaud, “Vibrational progressions in the visible and near-ultraviolet absorption spectrum of ozone,” Chem. Phys. Lett. 349, 241–248 (2001).
[CrossRef]

Isis (2)

D. C. Lindberg, “Roger Bacon’s theory of the rainbow: progress or regress?” Isis 57, 235–248 (1966).
[CrossRef]

R. C. Dales, “Robert Grosseteste’s scientific works,” Isis 52, 381–402 (1961).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Quant. Spectrosc. Radiat. Transfer (1)

P. Laven, “Simulation of rainbows, coronas and glories using Mie theory and the Debye series,” J. Quant. Spectrosc. Radiat. Transfer 89, 257–269 (2004).
[CrossRef]

Osiris (1)

C. B. Boyer, “Robert Grosseteste on the rainbow,” Osiris 11, 247–258 (1954).
[CrossRef]

Robert Grosseteste and His Intellectual Milieu (1)

Our dating is based on C. Panti, “Robert Grosseteste and Adam of Exeter’s physics of light, remarks on the transmission, authenticity and chronology of Grosseteste’s scientific opuscula,” in Robert Grosseteste and His Intellectual Milieu, J. Flood, J. Ginther, and J. Goering, eds. (Toronto, 2013), 165–190 at p. 185, Table 1, “A Tentative Chronology of Grosseteste’s Scientific Works.” Most commentators agree on the later dating, but not on the specific date-range: A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100–1700 (Oxford, 1953), p. 51: 1230–1235; R. W. Southern, Robert Grosseteste: The Growth of an English Mind in Medieval Europe, 2nd ed. (Oxford, 1992), p. 120: 1230–1233; R. C. Dales, “Robert Grosseteste’s Scientific Works,” Isis 52, 381–402, (1961) at 402: 1232–1235; J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983), at 655: 1230–1233.

Speculum (1)

J. J. McEvoy, “The chronology of Robert Grosseteste’s writings on nature and natural philosophy,” Speculum 58, 614–655 (1983).
[CrossRef]

Trans. Cambridge Philos. Soc. (1)

G. B. Airy, “On the intensity of light in the neighbourhood of a caustic,” Trans. Cambridge Philos. Soc. 6, Part 3, 397–403 (1838).

Other (14)

L. Baur, Die philosophischen Werke des Robert Grosseteste, Bischofs von Lincoln. Zum erstenmal vollständig in kritischer Ausgabe (Aschendorf, Münster, 1912).

D. C. Lindberg, “On the rainbow,” in A Source Book in Medieval Science, E. Grant, ed. (Harvard, 1974), pp. 388–391.

A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science 1100–1700 (Oxford University, 1953).

P. S. Anderson, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, H. E. Smithson, S. Sonnesyn, and B. K. Tanner, The Refraction of Rays: Robert Grosseteste’s De iride, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, Toronto (to be published).

G. Dinkova-Brunn, G. E. M. Gasper, M. Huxtable, T. C. B. McLeish, C. Panti, and H. E. Smithson, The Dimensions of Colour: Robert Grosseteste’s De colore, Durham Medieval and Renaissance Texts (Pontifical Institute of Mediaeval Studies, 2013).

J. J. Koenderink, Color for the Sciences (MIT, 2010).

Grosseteste uses here the Latin term lumen, not lux as he did in the De colore. Throughout his writings, Grossteste is careful to distinguish between source or essence of light (lux), and reflected light (lumen). To be faithful to this distinction, and to highlight to the modern reader that such a distinction exists in the Latin, we translate lumen here as “luminosity,” not “light.” However, our use of the word “luminosity” in this context should not be confused with the technical use of the term in modern vision science.

Similarly, he uses here admixtum cum, not incorporatum as he did in the De colore, which we translate as “mixed with,” not “embodied in.”

Grosseteste uses here the Latin adjective hyazinthinus, from the substantive hyacinthus, which we choose to translate as purple. The sources here are complex and are based on medieval references to gem stones and other color terminology. So, the identification with any particular color is blurred, but on-balance we believe that violet or purple with some red is an appropriate interpretation. The fact that in the (perceptual) hue circle (but not on a wavelength scale) violet, purple and red are adjacent is also worth noting.

R. Descartes, Discourse on Method, Optics, Geometry and Metereology, trans. P. J. Olscamp, ed., rev. (Hackett, 2001, orig. publ. 1965) Metereology, Eighth Discourse, pp. 332–345.

C. B. Boyer, The Rainbow: From Myth to Mathematics (Yoseloff, 1959).

J. D. Mollon, “The origins of modern color science,” in Color Science, S. Shevell, ed. (Optical Society of America, 2003).

The dominant wavelength of a particular spectral distribution is formally defined as the wavelength of monochromatic light that when added to a reference white light would produce a perceptual color match to the spectrum in question. A change in dominant wavelength is generally associated with a change in hue.

C. W. Allen, Astrophysical Quantities (Athlone, 1973).

Supplementary Material (4)

» Media 1: AVI (4723 KB)     
» Media 2: AVI (5621 KB)     
» Media 3: AVI (5743 KB)     
» Media 4: AVI (5576 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Plot of relative energy for scattering by a spherical droplet of water of radius r=200μm as a function of scattering angle for monochromatic sources (from 400 to 700 nm in steps of 20 nm producing 16 curves), and their sum (arbitrarily scaled by 0.25 for plotting). Curves are pseudo-colored to specify wavelength and the resultant color of the mixture.

Fig. 2.
Fig. 2.

Pseudo-color representation of the spectra obtained as a function of scattering angle (within a rainbow) and droplet radius (between rainbows).

Fig. 3.
Fig. 3.

Plots of the MacLeod–Boynton coordinates of spectra obtained by simulating scattering of light by spherical droplets of water, as occurs in natural rainbows. Each pseudo-colored symbol represents a particular combination of scattering angle and droplet size, according to the range represented in the Lee diagram of Fig. 2. Black lines are used to link points that share the same droplet size and are therefore characterized as within the same rainbow. (a) A projection onto the chromatic plane (Media 1). (b) An oblique projection, additionally showing the variation in (log) luminance (Media 1).

Fig. 4.
Fig. 4.

Plots of the CIELAB coordinates of spectra obtained by simulating scattering of light by spherical droplets of water, as occurs in natural rainbows. Each pseudo-colored symbol represents a particular combination of scattering angle and droplet size, according to the range represented in the Lee diagram of Fig. 2. Black lines are used to link points that share the same droplet size and are therefore characterized as within the same rainbow. The white-point is set to correspond to the daylight illuminant D65 at the maximum luminosity available within each rainbow. (a) A projection onto the chromatic plane (Media 2). (b) An oblique projection, additionally showing the variation in luminance (Media 2). (c) Analogous to (a), but including the spectral locus. (d) Analogous to (b) but including the spectral locus.

Fig. 5.
Fig. 5.

Plot of the CIELAB (a*,b*) coordinates of spectra obtained by simulating scattering of light by spherical droplet of water, as occurs in natural rainbows (Media 3). The white-point is set to correspond to the daylight illuminant D65 at the maximum luminosity available within each rainbow. A sparse grid of points is connected by lines with constant scattering angle (red) and constant droplet size (blue). These two sets constitute a possible coordinate system for the perceptual subspace spanned by possible rainbows generated from the unmodified solar spectrum.

Fig. 6.
Fig. 6.

Examples of “logarithmic-polar” coordinate systems generated from Eqs. (1) and (2) with various values of the tilt angle, ϕ. A value of ϕ=π/4 generates symmetric sets; decreasing values result in one set becoming tighter, the other looser, until the purely radial-circumferential system emerges in the limit of ϕ=0. A sign change in ϕ generates a change in the handedness of the system.

Fig. 7.
Fig. 7.

Effect of solar elevation angle on the solar spectrum and consequently on the rainbow locus. (a) The family of spectra (energy per unit wavelength) obtained with air mass values from 1.6 to 14.4 in steps of 0.8 (corresponding to solar elevation angles from 38.6° to 3.2° [26]) and ozone and aerosol factors of 1, based on the extinction model using molecular and aerosol scattering [27] and ozone absorption [28]. (b)–(d) The set of rainbow loci in CIELAB space that are produced by using these as the incident solar spectra (Media 4). The black lines give a skeleton outline of the surface that is obtained as a function of droplet size for the highest solar elevation. The red lines and colored symbols locate the surface that is obtained as a function of air mass for the smallest droplet size. The white-point is set to correspond to the daylight illuminant D65 at the maximum luminosity available within each rainbow.

Equations (2)

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x+iy=eρ+iθ,
y=y1+(tanϕ)xy=y1(cotϕ)x,

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