Grosseteste and an Ancient Optical PrincipleAuthor(s): Colin M. TurbayneSource: Isis, Vol. 50, No. 4 (Dec., 1959), pp. 467-472Published by: The University of Chicago Press on behalf of The History of Science SocietyStable URL: http://www.jstor.org/stable/226431 .Accessed: 09/05/2014 20:06

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Grosseteste and an Ancient Optical Principle

By Colin M. Turbayne *

A REVOLUTION in the history of science occurred in the thirteeth century A at Oxford. The man who started it was Robert Grosseteste (ca. 1168- 1253). "Grosseteste appears to have been the first medieval writer to recognize and deal with ... experimental verification" in science. Theories were to be re- tained only if they met the test of experience. By thus uniting the experimental habit with the Greek geometrical method, he and his successors "created mod- ern experimental science." The characteristic science in which he applied his ideas on method was optics. "He was the first medieval writer to discuss [optics] systematically."

These views are Dr. A. C. Crombie's, presented in his admirable Robert Grosseteste and the Origins of Experimental Science.' His argument, excep- tionally well documented, loses strength by his treatment of a fundamental point in Grosseteste's optics. The fundamental point is "The Ancient Prin- ciple," so named by Isaac Barrow in his Eighteen Lectures.2 This principle is as old as Euclid, and it stood until after Kepler. The question is: Did Grosse- teste subscribe to it or not? If he did, he was in the classical tradition. If not, he knew less about optics than his precursors: Euclid, Ptolemy, and the Arabs. Dr. Crombie does not give Grosseteste the credit for understanding it. I shall try to show that he did, first by sketching the history of the principle, and then by presenting Grosseteste's relevant remarks.

The Ancient Principle is a rule for locating the optical image in optical sys- tems after reflection or refraction. A concise eighteenth-century statement of it is as follows:

Any given visible point of an object appears at the intersection of the reflected or the refracted visual ray produced and of a line drawn through the visible point perpendicular to the reflecting or refracting surface whether plane or spherical.3

It is independent of the distinction, made by Kepler and now in general use, between the virtual and the real image. It is also independent of the emission and immission theories of vision (the former, that there are visual rays, was held, for example, by Plato and Euclid; the latter, by Democritus and Ari- stotle), and it appeared to work well enough with plane and spherical surfaces.

* University of Rochester, N. Y. I am in- debted to my colleague, Mr. John Stewart, for helpful advice on the subject matter of this paper.

1 Oxford, 1953. 2 Lectiones XVIII (London, 1669), lect. 18. 3 Robert Smith, A Compleat System of Op-

ticks (Cambridge, 1738), par. 212.

467

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468 COLIN M. TURBAYNE Euclid, in his Catoptrics4 (c. 300 B.C.), apparently understood The Ancient

Principle which his diagrams illustrate, because three of his theorems are de- ducible from it, though not, it seems to me, from his postulates.

IMAGE

OBJECT

IMAGE IMGE

MIRROR

EYE

OBjECT EYE OJC

EYE

FIG. 1 FIG. 2 FIG. 3

Th. 16 In plane mirrors the object appears on the perpendicular drawn from the object (fig. 1.)

Th. 17 In convex mirrors the object appears on the line drawn from the object to the center of the sphere (fig. 2.)

Th. 18 In concave mirrors the object appears on the line drawn from the ob- ject to the center of the sphere (fig. 3.)

Similar accounts were given by Ptolemy, Ibn al-Haitham, Witelo, and Roger Bacon. Ibn al-Haitham (who relinquished the emission theory) stated the principle as it applied to reflection: "In any plane, spherical convex, or spheri- cal concave mirror, the image is seen at the junction of the perpendicular of incidence and the reflected ray," I "the perpendicular of incidence" being an immissionist's name for Euclid's normal line drawn from the object to the surface of the plane mirror or to the center of the convex or concave mirror. In his, Bacon stated the principle as it applied to refraction: "Vision by re- fraction is at the intersection of the visual ray with the cathetus, as has been stated in regard to reflection," 6 "the cathetus" being a neutral name for the perpendicular of incidence. He used the principle to explain the bent appear- ance of the stick seen in water.

In 1604, Kepler' in his Supplement to Witelo, correctly rejected The Ancient Principle (though for incorrect reasons such as: if the mirror at its junction with the cathetus "is covered or blocked off [the image] can nevertheless be clearly seen,") in favor of new principles that become axioms 7 and 8 of New- ton's Opticks (1704) and the foundations of modern geometrical optics.7

Nevertheless, in his Catoptrics, the Jesuit mathematician, Andree Tacquet (1602-1660), tried to retain The Ancient Principle, "the most fecund in all catoptrics": "In plane and convex mirrors, any point of the object appears no- where else than at the intersection of the reflected ray with the perpendicular

4 Euclide: L'Optique et la Catoptrique, aeuvres traduites pour la premiere fois du grec en frangais par Paul Ver Eecke (Paris & Bruges, 1938); my translation.

5 Optica? Thesaurus Aihazeni Arabis ... a Federico Risnero (Basiliae, 1572), book 5,

chapter 2; my translation. 6 The Opus Majus, transl. by R. B. Burke

(Philadelphia, 1928), p. 565. 7 Ad Vitellionem Paralipomena, quibus As-

tronomiir pars Optica traditur (Frankfurt), chapter 3, 1; my translation.

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GROSSETESTE AND OPTICS 469 of incidence." 8 In treating reflection in concave mirrors, however, he found a certain odd case: "If the eye is between the center and the mirror, then ob- jects placed below the center make two images: an inverted one between the center and the mirror, and an erect one beyond the mirror [see fig. 4]." 1 The first image ("real" in modern optics) is accounted for by the principle, even though it may "appear" behind the eye, "but the second, though estab- lished by a sure experiment (experientia certa constet) no less than the first,

i

OBJECT FIG. 4

cannot be demonstrated from it" because this image "repeatedly appears out- side the junction of the reflected ray and the cathetus." '0 Having witnessed the collapse of The Ancient Principle, Tacquet could not bring himself to re- ject it outright: "In cave mirrors we postulate this only so far as its truth reveals itself"'1; and he left it at that.

Barrow, using Kepler's new principles (still basic to geometrical optics), found that they too were insufficient to explain not only Tacquet's case but also its complement for lenses; and he said:

Nor is our principle alone struck at by this experiment, but likewise all others that ever came to my knowledge are, every whit as much, endangered by it. The ancient one especially (which is most commonly received, and comes near-

8 Catoptrica tribus libris exposita, from his Opera mathematica, 2nd ed. (Antwerp, 1707), book 1, prop. 22; my translation.

9 Ibid., book 3, prop. 29. 10 Ibid., book 3, props. 29 and 30. 11 Ibid., book 3, prop. 22.

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470 COLIN M. TURBAYNE est to mine) seems to be so effectually overthrown thereby that the most learned Tacquet has been forced to reject that principle, as false and uncer- tain, on which alone he had built almost his whole Catoptrics; and conse- quently by taking away the foundation, hath himself pulled down the super- structure he had raised on it.12

Barrow could not bring himself to "renounce that which I know to be mani- festly agreeable to reason," and concluded that "in the present case some- thing peculiar lies hid, which being involved in the subtilty of nature will, per- haps, hardly be discovered till such time as the manner of vision is more per- fectly made known.""'

I now return to the question: Did Grosseteste subscribe to The Ancient Principle? Two passages, one from his On Lines, Angles, and Figures, the other from his On the Rainbow, reveal his views on refraction and reflection. The first is very general:

The ray falling [on another transparent body] at equal angles or perpendicu- larly keeps to a straight line of passage. But the one that falls at unequal angles deviates from the straight line.... This deviation is called the refraction of the ray.... If this second body is denser than the first, then the ray is re- fracted to the right and passes between the straight line of passage and the perpendicular drawn from the place of refraction on this second body."4

The diagram (fig. 5) copies Dr. Crombie's, for Grosseteste left none. It shows what Grosseteste probably intended: AO and OC are the incident and re- fracted rays, while AOE and COD are the angles of incidence and refraction.

In the second passage Grosseteste was more specific: That the size of the angle in the refraction of a ray may be thus determined, experiments show us similar to those by which we can discover that the re- flection of the ray falling on a mirror makes an angle equal to the angle of incidence.... A thing that is seen through the medium of several transparent bodies does not appear to be as it truly is, but appears to be at the junction betzween the ray passing out from the eye in continuous and direct projection, and the line coming from the thing seen wzhich falls on the surface of the second transparent body nearer the eye at equal angles on both sides. This is shown by the same experiment as, and similar reasoning to, those by which we know

12Barrow, op. cit., lect. 18; George Berk- eley's translation in his An Essay towards a New Theory of Vision (Dublin, 1709), sec. 29.

18 The second image that Barrow and Tac- quet saw is, indeed, inexplicable on the prin- ciples of ancient or modern geometrical optics, for, in terms of the one it is outside the junc- tion of the cathetus and the reflected ray, and in terms of the other it is neither real (the rays do not actually pass through it) nor sirtual (the rays cannot be projected to pass through it). This image or effigy, therefore, does not exist. Yet Barrow and Tacquet saw it, and anyone can confirm it. Two simi- lar criticisms of the foundations of modern optics have been made since Kepler fathered the science: one by Berkeley in 1709 (A New

Theory of Vision), and the other, independ- ently of him, by Professor Vasco Ronchi in 1955 (Optics: the Science of Vision [Bologna, 1955; New York, 1957]). Both offer solu- tions to what Berkeley called "The Barrovian Case" which, Berkeley claimed (sec. 33), "en- tirely subverts" the received theories, and which, Professor Ronchi concludes (sec. 192), modern optics is "utterly inadequate to ex- plain." See Colin Turbayne, "Berkeley and Ronchi on Optics," Proceedings XII Interna- tional Congress of Philosophy (in press).

14De lineis, angulis, et figuris, in L. Baur, Die philosophischen Werke des Robert Gros- seteste, Bischofs von Lincoln (Miinster, 1912), p. 63; Crombie's translation, op. cit., pp. 120-121, my italics.

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GROSSETESTE AND OPTICS 471

that things seen in a mirror appear at the junction of directly projected vision and the line coming to the surface of the mirror at an equal angle.15

This shows that Grosseteste subscribed to Euclid's law of reflection and emis- sion theory of vision. Thus, in figure 5, the incident ray projected is the same as the visual ray projected AOB. It shows also, it seems, that Grosseteste sub- scribed to The Ancient Principle, the junction being that of the visual ray projected and the cathetus.

But, in the absence of diagrams, another interpretation of this passage is possible: Grosseteste used the words, "The line coming from the thing seen ... ," to mean not the cathetus but the refracted ray. This view is adopted by Dr. Crombie: In figure 5, [By an observer at A] if an object were placed at C, it would be seen at 0, where BOC = COD." 16 In this view, a stick placed under water would be seen on the surface.'7 Accordingly, Dr. Crombie

E

A A

70 0

DENSER DENSER MEDIUM

,- ; MEDIUM C

B

C C

FIG. 5 FIG. 6

interprets Grosseteste's law of refraction for rays entering a denser medium: "The refracted ray bisects the angle between the projection of the incident ray and the perpendicular to the common surface at the point of entry of the incident ray into the denser medium," 18 or, which is the same thing, the angle of refraction equals half the angle of incidence. Thus, by the word "between" (inter) in the first passage, Grosseteste meant midway between. Having taken this view, and holding those views expressed in the first paragraph of this paper, Dr. Crombie is forced to conclude:

15 De iride, British Museum MS Royal 6.E.V., 14C., fols. 241r-vb; cf. Baur, op. cit., pp. 74-75; Crombie's translation, op. cit., p. 123, my italics. In the MS the italicized por- tions run as follows: Res autem, quae videtur per medium plurium perspicuorum, non ap- paret esse ut ipsa est secundum veritatem, sed apparet esse in concursu radii egredientis ab oculo in continuum et directum protractum et lineae ductae a re visa cadentis in super- ficiem secundi perspicui propinquiorem oculo

ad angulos sequales undique.... Res visae in speculis apparent in concursu visus directe protracti et lineae ductae super speculi super- ficiem ad angulos undique aequales.

16 Crombie, op. cit., p. 123. 17 This happens sometimes with lenses, and

with mirrors, as Professor Ronchi has pointed out, op. cit., secs. 128 and 170; but it is doubt- ful whether Grosseteste was aware of such exceptional cases.

18 Crombie, op. cit., p. 123.

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472 COLIN M. TURBAYNE Very simple experiments could have shown Grosseteste that his quantitative law of refraction was not correct. He was in fact, primarily a methodologist rather than an experimentalist.... Nevertheless, it was one of the basic prin- ciples of his theory of science that theories must be put to the test of experi- ment and that if they were contradicted by experiment then they had to be abandoned."'

However, in the light of my earlier account, it is far more likely that in the second passage, Grosseteste meant to state nothing but The Ancient Principle. "Commonly received" in classical optics, it would be astonishing if he had not subscribed to it. Certainly he read Euclid's Catoptrics20 (in which the dia- grams clearly illustrate the principle), probably Ptolemy's Optics, and pos- sibly Ibn al-Haitham's Book of Optics. In which case he intended the line coming from the thing seen to be the cathetus and not the refracted ray. This is confirmed by his use of linea for the line in question and radius for the ray. By the phrase "at equal angles on both sides" (ad angulos undique aequales) he obviously meant right angles. Compare the phrase "at equal angles or perpendicularly" (ad angulos aequales sive perpendiculariter) in the first passage. Accordingly, in figure 6, by an observer at A, if an object were placed at C, it would be seen at X where the visual ray AO, after "continuous and direct projection" intersects the cathetus CY. If this is so, then the passage does not reveal Grosseteste's law of refraction. But it does show a rule for finding the angle of refraction experimentally; it does show that he understood and accepted The Ancient Principle; and it is consistent with the view that he put his theories to the test of experiment.

19Ibid., p. 124. 20Called "De speculis" in his De natura

locorum and in his De iride; cf. Baur, op. cit.,

pp. 70 and 74, and Crombie, op. cit., pp. 116 and 119.

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Article Contentsp.467p.468p.469p.470p.471p.472

Issue Table of ContentsIsis, Vol. 50, No. 4 (Dec., 1959), pp. 417-530Volume Information [pp.524-529]Front Matter [pp.417-418]The Impact of Archimedes on Medieval Science [pp.419-429]Origin of the American Indian as Suggested by Fray Joseph de Acosta (1589) [pp.430-438]The Place of John Dumbleton in the Merton School [pp.439-454]Thomas Salusbury Discovered [pp.455-458]On the Presumed Darwinism of Alberuni Eight Hundred Years before Darwin [pp.459-466]Grosseteste and an Ancient Optical Principle [pp.467-472]Newton's Electric Spirit: Four Oddities [pp.473-476]Regula Philippi Arrhidaei [pp.477-478]Notes & Correspondence [pp.479-481]News of the Profession [pp.482-484]Book Reviewsuntitled [pp.484-486]untitled [pp.486-487]untitled [pp.487-488]untitled [pp.488-489]untitled [pp.489-492]untitled [pp.492-493]untitled [pp.493-494]untitled [pp.494-495]untitled [pp.495-496]untitled [pp.496-498]untitled [pp.498-499]untitled [pp.500-501]untitled [pp.501-502]untitled [pp.502-503]untitled [pp.503-504]untitled [pp.504-506]untitled [pp.506-507]untitled [pp.507-510]untitled [pp.510-511]untitled [pp.511-512]untitled [pp.512-514]untitled [pp.514-516]untitled [pp.516-517]untitled [pp.517-518]

Publications Received 1 March 1959 -- 1 September 1959 [pp.518-522]Errata: Evolution by Natural Selection [p.522]Back Matter [pp.523-530]