![]() ![]() Example of using low and high dispersion glasses in a doublet. Note that a low v value implies high dispersion. The London dispersion force is a temporary attractive force that results when the electrons in two adjacent atoms occupy positions that make the atoms form. Separation of colors by a prism is an example of dispersion.ĭispersion in optical glasses is typically characterized by index of refraction values at three standard wavelengths. dispersion: 1 n spreading widely or driving off Synonyms: scattering Types: Diaspora the dispersion of the Jews outside Israel from the destruction of the temple in Jerusalem in 587-86 BC when they were exiled to Babylonia up to the present time dissipation breaking up and scattering by dispersion Type of: spread, spreading process or result. MediumĬhromatic aberration arising from dispersion. The focal lengths shown are calculated from the lensmakers equation with radii of curvature 10.62 cm for both surfaces. The table below starts with a biconvex lens designed to have a focal length of 10.0 cm for violet light (400 nm) in crown glass. The effect of dispersion on the focal length of a lens can be examined by calculating the change in the focal length with wavelength. The dispersion is measured by a standard parameter known as Abbe's number, or the v value or V number, all of which refer to the same parameter:īlue light travels more slowly than red light in transparent media. Usually the dispersion of a material is characterized by measuring the index at the blue F line of hydrogen (486.1 nm), the yellow sodium D lines (589.3 nm), and the red hydrogen C line (656.3 nm). It also gives the generally undesirable chromatic aberration in lenses. Dispersion is the phenomenon which gives you the separation of colors in a prism. Generally the index decreases as wavelength increases, blue light traveling more slowly in the material than red light. Which just converts to the well-known relativistic equation $E^2=p^2 m^2$.Chromatic dispersion is the change of index of refraction with wavelength. For instance, the dispersion relation of the Klein-Gordon equation is just (in units with $\hbar$ and $c=1$) Since in quantum physics the energy is related to $\hbar \omega$, the dispersion relation captures some essential physical features of the problem. A wave of light has a speed in a transparent medium that. Ocean waves, for example, move at speeds proportional to the square root of their wavelengths these speeds vary from a few feet per second for ripples to hundreds of miles per hour for tsunamis. It is particularly important when the wave is not monochromatic, as all wavelength will propagate at slightly different frequencies, even is the medium is physically homogeneous. dispersion, in wave motion, any phenomenon associated with the propagation of individual waves at speeds that depend on their wavelengths. Thus, to answer specifically the question of the OP: dispersion does not measure the lack of homogeneity of a medium, but rather lack of simple linearity between $\omega$ and $k$. Eq.(1) is written to suggest it is the start of a Taylor expansion in $k^2$. The coefficient $\alpha$ would be $0$ is the string were perfectly elastic. Where $T_0$ is the tension in the string and $\rho_0$ is the linear density of the string. For instance, the frequency of a wave on a string is realistically related to the wave vector by In mechanical waves - like on a string or in air - the relation $\omega/k=$ constant is only a first order approximation (indeed a linear approximation in the sense that the associated wave equation is a linear PDE) and the true dispersion relation is more complicated. The best known example is the dispersion of light by a prism:Įven if the prism is made of homogeneous glass, the index of refraction of glass varies with $k$, leading to dispersion. Since $\omega/k$ is basically to the (phase) velocity of the wave, the dispersion relation describes the dependence of the phase velocity on the wavelength. The dispersion relation takes the form of a functional relation for $\omega(k)$ which is not, in general, linear. The dispersion relation expresses the relation between the wave vector $k$ and the frequency $\omega$. ![]()
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