Propagation direction speed

One way to accomplish this is by way of the Doppler effect. The wavelength at which an atom or molecule absorbs light will depend on the velocity of the molecule with respect to the propagation direction of the photon. If v0 is the rest absorption frequency, then v, the frequency at which the molecule with velocity v absorbs light with propagation direction kpr and speed c, is given by... 

Figure 2 The scattering problem illustrated for a spheroidal particle with orientation e and effective refractive index = n — i k. The surrounding medium is nonabsorbing, with the real refractive index ne, The speed of light within the medium is c = Co/r e, where Cq is the speed of light in vacuum. The incident plane wave has frequency v (ie, wavelength X = dv) and a wave vector collinear to o. A propagation direction of the radiation scattered by the particle is denoted as a. 0 is the angle between a and co. ...

Up to this point, we have calculated the linear response of the medium, a polarization oscillating at the frequency m of the applied field. This polarization produces its own radiation field that interferes with the applied optical field. Two familiar effects result a change in tlie speed of the light wave and its attenuation as it propagates. These properties may be related directly to the linear susceptibility The index of... 

When an isotropic material is subjected to planar shock compression, it experiences a relatively large compressive strain in the direction of the shock propagation, but zero strain in the two lateral directions. Any real planar shock has a limited lateral extent, of course. Nevertheless, the finite lateral dimensions can affect the uniaxial strain nature of a planar shock only after the edge effects have had time to propagate from a lateral boundary to the point in question. Edge effects travel at the speed of sound in the compressed material. Measurements taken before the arrival of edge effects are the same as if the lateral dimensions were infinite, and such early measurements are crucial to shock-compression science. It is the independence of lateral dimensions which so greatly simplifies the translation of planar shock-wave experimental data into fundamental material property information. 

The shock-change equation is the relationship between derivatives of quantities in terms of x and t (or X and t) and derivatives of variables following the shock front, which moves with speed U into undisturbed material at rest. The planar shock front is assumed to be propagating in the x (Eulerian spatial coordinate) or X (Lagrangian spatial coordinate) direction, p dx = dX. 

Refraction the change of direction of a ray of light in passing obliquely from one medium into another in which the speed of propagation differs. 

Within the elastic regime, the conservation relations for shock profiles can be directly applied to the loading pulse, and for most solids, positive curvature to the stress volume will lead to the increase in shock speed required to propagate a shock. The resulting stress-volume relations determined for elastic solids can be used to determine higher-order elastic constants. The division between the elastic and elastic-plastic regimes is ideally marked by the Hugoniot elastic limit of the solid. 

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