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THE MATHEMATICAL THEORY OF HUYGEN'S PRINCIPLE. B.B. Baker, E.T. Copson.
Publisher: Oxford University Press: 1950 2nd ed.

Descartes prescribed what the telescope should be according to mathematical theory. Luckily, diffraction is really very straightforward once one grasps said Huygens-Fresnel principle; the rest is just mathematical sleights of hand as we'll see. Finally, $\kappa$ is a “reality factor” to unite theory and observation, which we need to discuss a bit more in detail. The arbitrary assumptions made by Fresnel to arrive at the Huygens–Fresnel equation emerge automatically from the mathematics in this derivation. As can be seen from the schedule, the workshop was concerned with mathematical questions to do with the geometry of quantum states in the standard Hilbert space picture of quantum mechanics, rather than any physical issues that is only tenuously understandable, and is a minor quirk of theory that doesn't at all matter in practice (just the way I can always apply Huygens' principle also in 2D—following another definition of the principle: a local definition). A simple example of the operation of the principle can be seen Using Huygens' theory and the principle of superposition of waves, the complex amplitude at a further point P is found by summing the contributions from each point on the sphere of radius r0. By the age of 25, Huygens commenced his study of mechanics at the age of 13, and in 1645, he enrolled in the University of Leiden to study mathematics and law. Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century, Fokko Jan Dijksterhuis. A word of warning: While most of the following is extracted from books and other public sources, I make . Huy-gens's principle posits the existence of two "wave fronts," one primary and one secondary, which accounted for both reflection and refraction of light. Christiaan Huygens fueled the Scientific Revolution with his wide-ranging scientific contributions, from astronomical observations to theories of mechanical physics. Figure 3: Geometry of the diffraction problem, as described by (3).