Fermat’s principle in constant gravitational field

Recently (Int. J. Mod. Phys. D 27 (2018) 1847025) an interesting property of closed light rings in Kerr black holes has been noticed. We explain its origin and derive a slightly more general result.

Aristotle Redivivus

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.

Fresnel Diffraction

Fresnel diffraction is discussed in terms of a description of waves traveling near the stationary point. That is the point that lies on a line connecting the source and the observation point. We discuss a rectangular aperture using Fresnel integrals or graphicly using the Cornu Spiral We discuss a circular aperture in terms of Fresnel zones and we develop a simple formula for the calculation of the radius of a Fresnel zone. Using the concept of Fresnel zones we develop an expalination of Fermat’s Principle and explain the origin of Poisson’t spot. The Fresnel zones generate an understanding of the operation of the pinhole camera.