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Here ψ is the angle between the path of the wave source and the direction of wave propagation (the wave vector k), and the circles represent wavefronts. Consider one of the phase circles of Fig.12.3 for a particular k , corresponding to the time t in the past, Fig.12.2.
The Gaussian function has a 1/e 2 diameter (2w as used in the text) about 1.7 times the FWHM.. At a position z along the beam (measured from the focus), the spot size parameter w is given by a hyperbolic relation: [1] = + (), where [1] = is called the Rayleigh range as further discussed below, and is the refractive index of the medium.
[1] This pattern consists of two wake lines that form the arms of a chevron, V, with the source of the wake at the vertex of the V. For sufficiently slow motion, each wake line is offset from the path of the wake source by around arcsin(1/3) = 19.47° and is made up of feathery wavelets angled at roughly 53° to the path.
In Laue geometry, beam paths lie within the Borrmann triangle. Kato fringes are the intensity patterns due to Pendellösung effects at the exit surface of the crystal. Anomalous absorption effects take place due to a standing wave patterns of two wave fields. Absorption is stronger if the standing wave has its anti-nodes on the lattice planes ...
Full width at half maximum. In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value.
A light ray is a line or curve that is perpendicular to the light's wavefronts (and is therefore collinear with the wave vector). A slightly more rigorous definition of a light ray follows from Fermat's principle, which states that the path taken between two points by a ray of light is the path that can be traversed in the least time. [1]
In Riemannian geometry and pseudo-Riemannian geometry, the Gauss–Codazzi equations (also called the Gauss–Codazzi–Weingarten-Mainardi equations or Gauss–Peterson–Codazzi formulas [1]) are fundamental formulas that link together the induced metric and second fundamental form of a submanifold of (or immersion into) a Riemannian or pseudo-Riemannian manifold.
For a given Mach number, M 1, and corner angle, θ, the oblique shock angle, β, and the downstream Mach number, M 2, can be calculated. Unlike after a normal shock where M 2 must always be less than 1, in oblique shock M 2 can be supersonic (weak shock wave) or subsonic (strong shock wave). Weak solutions are often observed in flow geometries ...