Dioptrique

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First page of "La dioptrique" by Rene Descartes Descartes-1637-b001 (1).jpg
First page of "La dioptrique" by René Descartes

"La dioptrique" (in English "Dioptrique", "Optics", or "Dioptrics"), is a short treatise published in 1637 included in one of the Essays written with Discourse on the Method by Rene Descartes. In this essay Descartes uses various models to understand the properties of light. This essay is known as Descartes' greatest contribution to optics, as it is the first publication of the Law of Refraction. [1]

<i>Discourse on the Method</i> book by Descartes

Discourse on the Method of Rightly Conducting One's Reason and of Seeking Truth in the Sciences is a philosophical and autobiographical treatise published by René Descartes in 1637. It is best known as the source of the famous quotation "Je pense, donc je suis", which occurs in Part IV of the work. A similar argument, without this precise wording, is found in Meditations on First Philosophy (1641), and a Latin version of the same statement Cogito, ergo sum is found in Principles of Philosophy (1644).

Contents

First Discourse: On Light

Page of Descartes' "La dioptrique" with the wine vat example. Descartes-1637-b006 (1).jpg
Page of Descartes' "La dioptrique" with the wine vat example.

The first discourse captures Descartes' theories on the nature of light. In the first model, he compares light to a stick that allows a blind person to discern his environment through touch. Descartes says:

Light electromagnetic radiation in or near visible spectrum

Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to visible light, which is the visible spectrum that is visible to the human eye and is responsible for the sense of sight. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), or 4.00 × 10−7 to 7.00 × 10−7 m, between the infrared and the ultraviolet. This wavelength means a frequency range of roughly 430–750 terahertz (THz).

You have only to consider that the differences which a blind man notes among trees, rocks, water, and similar things through the medium of his stick do not seem less to him than those among red, yellow, green, and all the other colors seem to us; and that nevertheless these differences are nothing other, in all these bodies, than the diverse ways of moving, or of resisting the movements of, this stick. [2]

Descartes' second model on light uses his theory of the elements to demonstrate the rectilinear transmission of light as well as the movement of light through solid objects. He uses a metaphor of wine flowing through a vat of grapes, then exiting through a hole at the bottom of the vat.

Now consider that, since there is no vacuum in Nature as almost all the Philosophers affirm, and since there are nevertheless many pores in all the bodies that we perceive around us, as experiment can show quite clearly, it is necessary that these pores be filled with some very subtle and very fluid material, extending without interruption from the stars and planets to us. Thus, this subtle material being compared with the wine in that vat, and the less fluid or heavier parts, of the air as well as of other transparent bodies, being compared with the bunches of grapes which are mixed in, you will easily understand the following: Just as the parts of this wine...tend to go down in a straight line through the hole [and other holes in the bottom of the vat]...at the very instant that it is open...without any of those actions being impeded by the others, nor by the resistance of the bunches of grapes in this vat...in the same way, all of the parts of the subtle material, which are touched by the side of the sun that faces us, tend in a straight line towards our eyes at the very instant that we open them, without these parts impeding each other, and even without their being impeded by the heavier particles of transparent bodies which are between the two. [2]

Second Discourse: On Refraction

Page of Descartes' "La dioptrique" with the tennis ball example. Descartes-1637-b011.jpg
Page of Descartes' "La dioptrique" with the tennis ball example.

Descartes uses a tennis ball to create a proof for the laws of reflection and refraction in his third model. This was important because he was using real-world objects (in this case, a tennis ball) to construct mathematical theory. Descartes' third model creates a mathematical equation for the Law of Refraction, characterized by the angle of incidence equalling the angle of refraction. In today's notation, the law of refraction states,

Reflection (physics) change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated

Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Mirrors exhibit specular reflection.

Refraction refraction of light

In physics refraction is the change in direction of a wave passing from one medium to another or from a gradual change in the medium. Refraction of light is the most commonly observed phenomenon, but other waves such as sound waves and water waves also experience refraction. How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed.

sin i = n sin r, where i is the angle of incidence, r is the angle of refraction, and n is the index of refraction. Using a tennis ball, Descartes would compare the projection of a ray of light to the way a ball moves when it is thrown up against another object.

Controversy

The astronomer Jean-Baptiste Morin was noted as one of the first people to question Descartes' method in creating his theories.

Jean-Baptiste Morin (mathematician) French astronomer

Jean-Baptiste Morin, also known by the Latinized name as Morinus, was a French mathematician, astrologer, and astronomer.

...Descartes would not accept Morin's objections that the demonstrations in the Dioptric are circular or that the proposed explanations are artificial. He grants that 'to prove some effects by a certain cause, then to prove this cause by the same effects', is arguing in a circle; but he would not admit that it is circular to explain some effects by a cause, and then to prove that the cause by the same effects, 'for there is a great difference between proving and explaining'. Descartes points out that he used the word 'demonstration'...to mean either one or the other 'in accordance with common usage, and not in the particular sense given to it by Philosophers'. Then he adds: 'it is not a circle to prove a cause by several effects which are known otherwise, then reciprocally to prove some other effects by this cause'. [3]


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References

  1. Osler, Margaret J (2010). Reconfiguring the World: Nature, God, and Human Understanding from the Middle Ages to Early Modern Europe. Baltimore, Maryland: The Johns Hopkins University Press. pp. 105–110. ISBN   978-0-8018-9656-9.
  2. 1 2 Descartes, René (1637). Discourse on Method, Optics, Geometry, and Meteorology.
  3. Sabra, A.I. (1981). Theories of Light from Descartes to Newton. Cambridge: Cambridge University Press. pp. 17–23. ISBN   0521240948.