Light, wave theory velocity

The refractive index of a substance is, of course, a relative expression, as it refers to a second substance, which, in ordinary determinations, is always the air. The term refractive index indicates the ratio of the velocities with which light traverses the two media respectively. This is, as is easily demonstrated by a consideration of the wave theory of light, identical with the ratio of the sine of the angle of incidence, and the sine of the angle of refraction, thus—... 

Electromagnetic radiation travels in straight lines in a uniform medium, has a velocity of 299,792,500 m/sec in a vacuum, and possesses properties of a wave motion and also of a particle (photon). The wave theory of light can satisfactorily account for properties such as wavelength, interference, refraction, polarization, reflection, and diffraction. 

This section explains impedance and admittance formulas of nonuniform lines, such as finite-length horizontal and vertical conductors based on a plane wave assumption. The formulas are applied to analyze a transient on a nonuniform line by an existing circuit theory-based simulation tool such as the EMTP [9,11]. The impedance formula is derived based on Neumann s inductance formula by applying the idea of complex penetration depth explained earlier. The admittance is obtained from the impedance assuming the wave propagation velocity is the same as the light velocity in free space in the same manner as an existing admittance formula, which is almost always used in steady-state and transient analyses on an overhead line. 

The next great development in physics was again an outgrowth of Einstein s ideas. Dirac was not satisfied with the fact that early quantum mechanics did not fit into the framework of relativity theory, The velocities of electrons in ordinary atoms are so small compared to the speed of light that the neglect of relativity theory did not matter much. Rut what about wave mechanics of particles that move much faster Dirac was able in 1927 to unite relativity with quantum mechanics. 

The uncertainty principle shows that the classical trajectory of a particle, with a precisely determined position and momentum, is really an illusion. It is a very good approximation, however, for macroscopic bodies. Consider a particle with mass I Xg, and position known to an accuracy of 1 pm. Equation 2.41 shows that the uncertainty in momentum is at least 5 x 10 29 kg m s-1, corresponding to a velocity of 5 x 10 JO m s l. This is totally negligible for any practical purpose, and it illustrates that in the macroscopic world, even with very light objects, the uncertainty principle is irrelevant. If we wanted to, we could describe these objects by wave packets and use the quantum theory, but classical mechanics gives essentially the same answer, and is much easier. At the atomic and molecular level, however, especially with electrons, which are very light, we must abandon the idea of a classical trajectory. The statistical predictions provided by Bom s interpretation of the wavefunction are the best that can be obtained. 

The applicability of the Stockmayer-Hecht theory is illustrated in Fig. 2 where Tm required to bring about agreement between theory and experiment is plotted as a function of T. For perfect agreement Tm should be a constant. The straight lines indicate the values of Tm that are approximately constant. Inasmuch as Tm equals hcwave numbers, the latter can be calculated for the two polymers. The result of this calculation is... 

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