Abstract
In Bk. 17, Ch. 4 of Magia Naturalis (1589) Giambattista Della Porta (ca. 1535–1615) reported his experiments on concave spherical mirrors arranged in various setups. Della Porta identified two critical points: (1) the point of inversion (punctum inversionis) in reference to the place where the magnified image is turned upside down and seen blurred, and (2) the point of burning (punctum incensionis) in reference to the place where the reflected rays concentrate and ignite fire. Opticians and practitioners of the time distinguished between the two points but considered them to occupy the same spatial location.
Della Porta inferred from his studies of concave spherical mirrors that the position of the point of inversion and that of the point of burning occupy different spatial locations. He associated the point of inversion with a locus where the image is seen magnified, turned upside down and blurred—a matter of visual perception. He defined the point of burning as a physical, optical position associated with a geometrical point in which the converging rays ignite fire. Consequently, throughout Bk. 17, Della Porta discarded the point of inversion from his optical nomenclature and referred only to the point of burning, the real—so to speak—optical point. In so doing, Della Porta contributed fundamentally towards the technological management of sets of optical elements.
In this paper we follow the experimental practice of Della Porta as presented by the optical demonstrations in Bk. 17, Ch. 4. We discuss the theoretical principles Della Porta developed to clarify whether his claim concerning concave spherical mirror is hypothetical or was it based on an inference from experience. We offer novel insights into the development of the theory of reflection in concave spherical mirrors as it was pursued by Della Porta. He eliminated perceptual considerations from his optics and considered only geometrical-physical aspects. This approach was most useful in the development of the telescope where the critical aspect is not perception but rather ratio of spatial angles.
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- 1.
Della Porta (1589, Bk. 17: 264–265).
- 2.
Della Porta (1593, Bk. 2: 39–41).
- 3.
In addition to Cardano, Della Porta also referred to, among others, Alhacen, Archimedes, Aristotle, Euclid, Galen, Pecham, Ptolemy, Vesalius, and Witelo as sources for his knowledge of optics.
- 4.
- 5.
- 6.
- 7.
Della Porta (1589, Bk. 17: 265, 271).
- 8.
- 9.
Della Porta (1593, Bk. 2: 36–41).
- 10.
On the law of reflection, see Smith (2015: 55–59).
- 11.
In Bk. 2 of De Refractione, Della Porta introduced the reciprocity between reflection and refraction as the framework for his study of refraction. For that purpose Della Porta explored and physically illustrated phenomena of reflection and refraction in mirrors and glass spheres which he thought could illustrate the visual faculties. See Zik and Hon (2012: 445–456); Smith (2015: 347–349).
- 12.
- 13.
Della Porta (1589, Bk. 17: 267): “In nostris in opticis fusius declaratum est.”
- 14.
Della Porta (1589, Bk. 17, Ch. 22: 279). Note that Della Porta’s technical instructions given in chapters 17–21, and 23, include detailed account for the production of parabolic mirrors, optical elements of cylindrical shape, spectacles lenses, and looking mirrors made of glass or metal: see Della Porta (1589, Bk. 17: 275–280).
- 15.
On Della Porta and his optical experience in Venice, see Reeves (2008: 70–78).
- 16.
Crasso (1666, Vol. 2: 297).
- 17.
Della Porta (1589, Bk. 17: 264–265).
- 18.
In effect this is the place where the point of burning (focal point) of the mirror is located.
- 19.
Della Porta (1589, Bk. 17: 264).
- 20.
Here Della Porta was still considering the point of inversion and the point of burning occupying the same place at the center of the mirror.
- 21.
On the cathetus rule of image formation, see Smith (2015: 59–62).
- 22.
Della Porta (1589, Bk. 17: 264).
- 23.
Della Porta (1589, Bk. 17: 265).
- 24.
Della Porta ([1558] 1562, Bk. 4, Ch. 14: 125): “Si verò maioris sphæræ fuerit segmentum, per maiorem accendit distantiam.”
- 25.
Della Porta (1589, Bk. 17: 266): “Id tamen duximus ad monedum, neoperam frustreris, quod proportionati sint oportet circuli specilli & concaui portio.”
- 26.
Della Porta (1589, Bk. 17: 267): “Nec leues poterunt imaginari technae, distantiam speculi magnitudine emendabis. Sat habes, qui id docere conati sunt, non nisi nugas protulere, necaliquibus ad huc compertum putarim.”
- 27.
The optical properties of the mirror we used in the simulations are: radius curvature 54 cm, diameter 15 cm, and focal length 27 cm. For measuring the distances among the elements in the test we used an optical bench. The computations throughout this paper were made with OSLO (Optical Software for Layout and Optimization).
- 28.
- 29.
Della Porta (1593, Bk. 2: 40): “Vt libro naturalis Magiae demonstrauimus.”
- 30.
Della Porta (1593, Bk. 2: 39, 41).
- 31.
Della Porta (1589, Bk. 17: 271).
- 32.
See, Densmore (2002, Bk. 4: 83–98).
- 33.
Della Porta (1593, Bk. 2: 39).
- 34.
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Acknowledgments
We gratefully acknowledge the helpful correspondence and ensuing discussions with A. Mark Smith and his critical comments related to the translation of Della Porta’s De Refractione. This research is supported by the Israel Science Foundation (Grant No. 67/09).
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Zik, Y., Hon, G. (2017). Giambattista Della Porta: A Magician or an Optician?. In: Borrelli, A., Hon, G., Zik, Y. (eds) The Optics of Giambattista Della Porta (ca. 1535–1615): A Reassessment. Archimedes, vol 44. Springer, Cham. https://doi.org/10.1007/978-3-319-50215-1_3
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