I’ve just finished reading selections from another work by Sir Isaac Newton, Optics, guided by what Mortimer J. Adler and Peter Wolff say about it in Foundations of Science and Mathematics, Reading Plan 3 of Encyclopedia Britannica’s The Great Ideas Program (Encyclopedia Britannica, 1960). In the Reading Plan Mortimer J. Adler and Peter Wolff (I) compare the methods used by Newton in Mathematical Principles and Optics; (II) examine the law of reflection and the law of refraction; (III) consider the corpuscular and wave theories of light; and (IV) pose and discuss three questions. Here I’ll compare the methods used by Newton (summarizes I), outline the parts of Optics assigned for reading in Foundations of Science and Mathematics (includes II and III), compare the corpuscular and wave theories of light (summarizes III), and pose the questions asked in IV. For a sketch of Newton’s life see https://opentheism.wordpress.com/2019/07/12/12-newtons-mathematical-principles-of-natural-philosophy/.
The Methods Used by Newton
Both of the works of Newton considered in my readings from Great Books of the Western World, Mathematical Principles of Natural Philosophy (https://opentheism.wordpress.com/2019/07/12/12-newtons-mathematical-principles-of-natural-philosophy/) and Optics, follow the pattern of Euclid’s Elements (https://opentheism.wordpress.com/2018/04/06/1-2-euclids-elements/): they begin with definitions, axioms, and postulates and then they present a series of propositions. However they differ considerably from each other in method. Mathematical Principles is a work in mathematical physics, characterized by the mathematical development of certain tentative formulations. Optics is a work in experimental physics, characterized by the experimental development of certain general principles.
All three works employ axioms, but they are of different kinds. The axioms in Elements are self-evident truths that are universally applicable. The axioms in Mathematical Principles state the very general Laws of Motion, which form the basis of the entire science of dynamics. The axioms in Optics just state what was generally accepted in the science of optics around the year 1700.
All three works present propositions, but again they are of different kinds. The propositions in Elements and Mathematical Principles state conclusions that are to be demonstrated from general principles. Optics state principles that have been found as the result of making experiments and observations and drawing general conclusions from them by induction.
[The above is based on part I of Adler and Wolff’s guide to Optics (Foundations of Science and Mathematics, pages 181-184).]
This is an outline of the parts of Optics assigned for reading in Foundations of Science and Mathematics: Book I, Part I, Definitions, Axioms, Propositions 1-2; Book III, Part I, Queries 27-31.DEFINITIONS
Newton defines eight terms. If I use a term which you don’t know the meaning of, please ask me its meaning and if it’s a term which Newton defines, I’ll give you his definition of it.AXIOMS
Newton gives eight axioms. I’ll give here just the three which Adler and Wolff explain or refer to in Part II of their guide to Optics (Foundations of Science and Mathematics, pages 184-186).
II. The angle of reflexion is equal to the angle of incidence.
IV. Refraction out of the rarer medium into the denser is made towards the perpendicular; that is, so that the angle of refraction be less than the angle of incidence.
V. The sine of incidence is either accurately or very nearly in a given ratio to the sign of refraction.
Newton presents 39 propositions but only the first two are assigned for reading in Foundations of Science and Mathematics. They are:PROPOSITIONS
Newton presents 39 propositions but only the first two are assigned for reading in Foundations of Science and Mathematics. They are:
1. Lights which differ in colour, differ also in degrees of refrangibility. [Under Definitions, Newton defines refrangibility of rays of light as “their disposition to be refracted or turned out of their way in passing out of one transparent body or medium into another” (Optics in Great Books of the Western World, Encyclopedia Britannica, 1952, volume 34, page 379).]
2. The light of the Sun consists of rays differently refrangible.
In conjunction with presenting the 39 propositions, Newton makes 38 observations. After making them, he planned to repeat most of them and to make more to determine how rays of light are bent in their passage by bodies. However he was interrupted and instead proposed some queries to assist others in their search. The last five of his 31 queries are assigned for reading in Foundations of Science and Mathematics. They are:
27. Are not all hypotheses erroneous which have hitherto been invented for explaining the phenomena of light, by new modifications of the rays?
28. Are not all hypotheses erroneous in which light is supposed to consist in pressure or motion, propagated through a liquid fluid?
29. Are not the rays of light very small bodies emitted from shining substances?
30. Are not gross bodies and light convertible into one another, and may not bodies receive much of their activity from the particles of light which enter their composition?
31. Have not the small particles of bodies certain powers, virtues, or forces, by which they act at a distance, not only upon the rays of light for reflecting, refracting, and inflecting them, but also upon one another for producing a great part of the phenomena of Nature?
Adler and Wolff consider these queries in their III, which I summarize below.
The Corpuscular and Wave Theories of Light
In Query 29 (see above) Newton refers to the corpuscular theory of light, adding, “For such bodies will pass through uniform mediums in rights lines without bending into the shadow, which is the nature of the rays of light.” Adler and Wolff observe that this characteristic of light is easily explained by the corpuscular theory of light but gives some difficulty to its great rival, the wave theory of light, which will be encountered in the next reading in this series.
One consequence of the corpuscular theory is that light travels more swiftly in a denser than in a rarer medium. However according to the wave theory light travels more rapidly in a rarer medium than in a denser one. In 1850 Foucault performed an experiment which showed that the speed of light is greater in air than in water, thus supporting the wave theory. However since then additional phenomena have been discovered which cannot be reconciled with the wave theory. Thus the nature of light is still in doubt.
Questions about the Reading
1. What is the method employed by Newton to prove the axioms in the Optics?
2. How does the law of refraction explain the bent appearance of a stick in water?
3. Are there any practical consequences of the different refrangibility [capability of being refracted] of light rays of different color?