منابع مشابه
Reflection, Refraction and the Prism
Huygens’ principle can be used to determine various experimentally verifiable and predictable behavior of the path of light through any optical system. However, as seen in the chapter on Light, the Huygens wavefront construction can be become complicated, especially in systems with a large number of optical components. A simpler approach to track the behavior of light is based on the propagatio...
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We construct in dimension two a mirror that reflects collimated rays into a set of directions that amplify the image and an optical lens so that collimated rays are refracted into a set of directions with a prescribed magnification factor. The profiles of these optical surfaces are given by explicit formulas involving the Legendre transformation.
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Hamiltonian Monte Carlo (HMC) is a successful approach for sampling from continuous densities. However, it has difficulty simulating Hamiltonian dynamics with non-smooth functions, leading to poor performance. This paper is motivated by the behavior of Hamiltonian dynamics in physical systems like optics. We introduce a modification of the Leapfrog discretization of Hamiltonian dynamics on piec...
متن کاملRefraction and reflection of diffusion fronts.
Diffusion waves form the basis of several measurement technologies in materials science as well as in biological systems. They are, however, so heavily damped that their observation is a real challenge to the experimentalist. We show that accurate information about the refraction-like and reflection-like behavior of diffusion waves can be obtained by studying diffusion fronts. For this we use h...
متن کاملInfluence of boundary reflection and refraction on diffusive photon transport.
We report computer simulations which test the accuracy of the diffusion theories used in the analysis of multiple light scattering data. Explicitly including scattering anisotropy and boundary reflections, we find that the predicted probability for transmission through a slab is accurate to 1% if the slab thickness is greater than about 5 transport mean free paths. For strictly isotropic scatte...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 1888
ISSN: 0024-6115
DOI: 10.1112/plms/s1-20.1.351