Aristotle Redivivus

On Purpose ◽  
2019 ◽  
pp. 129-152
Author(s):  
Michael Ruse
Keyword(s):  
Scientific Revolution ◽  
Dense Medium ◽  
Angle Of Incidence ◽  
Final Cause ◽  
Shortest Distance ◽  
Fermat’S Principle ◽  
Snell’S Law ◽  
Snell's Law ◽  
Fermat's Principle

This chapter explains occurrences during and after the Scientific Revolution, in which the personification of nature that is at the heart of the Aristotelian philosophy had a nasty way of reappearing in the most orthodox of machine-metaphor- influenced places. Even more than mechanics, optics was riddled with final-cause thinking. Pierrre de Fermat's “principle of least time” explains Snell's law of refraction, the connection between the angle of incidence and the angle of refraction. Since light going from a less dense to a denser medium is bent toward the normal, it is not going from beginning to end by the shortest distance. But assuming that light travels less quickly in a more dense than less dense medium, one can show that it does travel in the shortest time.

Huygens' Principle: A case against optimality

2003 ◽  
Vol 26 (6) ◽  
pp. 779-781
Author(s):  
Hans-Martin Gaertner
Keyword(s):  
Conceptual Problem ◽  
Present Evidence ◽  
Fermat’S Principle ◽  
Huygens Principle ◽  
Snell’S Law ◽  
Snell's Law ◽  
Fermat's Principle

I will present evidence that nature does not optimize in the sense of Fermat's principle of least time, contrary to what Schoemaker's unintentionally ambiguous exposition might suggest. First, Huygens' principle, an alternative nonteleological account of Snell's law, is outlined. Second, I confront Fermat's principle with a substantive conceptual problem.

On Fermat’s principle and Snell’s law in lossy anisotropic media

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. T107-T116 ◽  
Author(s):  
José M. Carcione ◽  
Bjorn Ursin
Keyword(s):  
Electromagnetic Waves ◽  
Heterogeneous Media ◽  
Transversely Isotropic ◽  
Slowness Vector ◽  
First Case ◽  
Fermat’S Principle ◽  
Snell’S Law ◽  
Snell's Law ◽  
Fermat's Principle ◽  
Homogeneous Media

Fermat’s principle of least action is one of the methods used to trace rays in inhomogeneous media. Its form is the same in anisotropic elastic and anelastic media, with the difference that the velocity depends on frequency in the latter case. Moreover, the ray, envelope, and energy velocities replace the group velocity because this concept has no physical meaning in anelastic media. We have first considered a lossy (anelastic) anisotropic medium and established the equivalence between Fermat’s principle and Snell’s law in homogeneous media. Then, we found that the different ray velocities defined in the literature were the same for stationary rays in homogeneous media, with phase and inhomogeneity angles satisfying the principle and the law. We considered an example of a transversely isotropic medium with a vertical symmetry axis and wavelike and diffusionlike properties. In the first case, the differences were negligible, which was the case of real rocks having a quality factor greater than five. Strictly, ray tracing should be based on the so-called stationary complex slowness vector to obtain correct results, although the use of homogeneous viscoelastic waves (zero inhomogeneity angle) is acceptable as an approximation for earth materials. However, from a rigorous point of view, the three velocities introduced in the literature to define the rays present discrepancies in heterogeneous media, although the differences are too small to be measured in earth materials. The findings are also valid for electromagnetic waves by virtue of the acoustic-electromagnetic analogy.

A computer based experiment to show that Snell’s law follows from Fermat’s principle

2019 ◽  
Vol 54 (5) ◽  
pp. 055019
Author(s):  
Sushil Kumar Singh ◽  
Jaya Shivangani Kashyap ◽  
Priyanka Rajwani ◽  
Savinder Kaur
Keyword(s):  
Computer Based ◽  
Fermat’S Principle ◽  
Snell’S Law ◽  
Snell's Law ◽  
Fermat's Principle

ELECTROMAGNETIC LATERAL WAVES OBSERVED BY EARTH‐SOUNDING RADARS

Geophysics ◽  
1976 ◽  
Vol 41 (6) ◽  
pp. 1126-1132 ◽  
Author(s):  
John W. Clough
Keyword(s):  
Electromagnetic Waves ◽  
Critical Angle ◽  
Continuous Wave ◽  
Angle Of Incidence ◽  
Lateral Wave ◽  
Snell’S Law ◽  
Snell's Law ◽  
Low Amplitude

Electromagnetic waves refracted at the critical angle according to Snell's law give rise to the lateral wave. The low amplitude lateral wave is usually obscured by other waves when continuous wave sources are used. Using a pulsed source (radar) and continuously recording echoes reflected from within dielectric earth materials as a function of angle of incidence, records are produced which clearly show the lateral wave. In some earth‐probing applications, the lateral wave may predominate and proper identification of its characteristics is important.

scholarly journals Snell's law for spin waves at a 90° magnetic domain wall

2020 ◽  
Vol 116 (11) ◽  
pp. 112402 ◽  
Author(s):  
Tomosato Hioki ◽  
Rei Tsuboi ◽  
Tom H. Johansen ◽  
Yusuke Hashimoto ◽  
Eiji Saitoh
Keyword(s):  
Domain Wall ◽  
Spin Waves ◽  
Magnetic Domain ◽  
Magnetic Domain Wall ◽  
Snell’S Law ◽  
Snell's Law

Quantitative OCT image correction using Fermat's principle and mapping arrays

2002 ◽  
Author(s):  
Volker Westphal ◽  
Sunita Radhakrishnan ◽  
Andrew M. Rollins ◽  
Joseph A. Izatt
Keyword(s):  
Image Correction ◽  
Fermat’S Principle ◽  
Fermat's Principle ◽  
Mapping Arrays ◽  
Oct Image
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