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is the speed of light (i.e. phase velocity) in a medium with permeability μ, and permittivity ε, and ∇ 2 is the Laplace operator. In a vacuum, v ph = c 0 = 299 792 458 m/s, a fundamental physical constant. [1] The electromagnetic wave equation derives from Maxwell's equations.
Sometimes c is used for the speed of waves in any material medium, and c 0 for the speed of light in vacuum. [10] This subscripted notation, which is endorsed in official SI literature, [ 11 ] has the same form as related electromagnetic constants: namely, μ 0 for the vacuum permeability or magnetic constant, ε 0 for the vacuum permittivity ...
The equations simplify slightly when a system of quantities is chosen in the speed of light, c, is used for nondimensionalization, so that, for example, seconds and lightseconds are interchangeable, and c = 1. Further changes are possible by absorbing factors of 4π.
The absolute refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, c = 299 792 458 m/s, and the phase velocity v of light in the medium, =. Since c is constant, n is inversely proportional to v : n ∝ 1 v . {\displaystyle n\propto {\frac {1}{v}}.}
It is possible to make the effective speed of light dependent on wavelength by making light pass through a material which has a non-constant index of refraction, or by using light in a non-uniform medium such as a waveguide. In this case, the waveform will spread over time, such that a narrow pulse will become an extended pulse, i.e., be dispersed.
Descartes assumed the speed of light was infinite, yet in his derivation of Snell's law he also assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e., the speed of light is finite, and his derivation depended upon the speed of light being slower in a denser medium.
Defining equation SI units Dimension ... λ = wavelength of light in medium, v = speed of light in media. Polarization. Physical situation Nomenclature Equations
In a uniform medium if the permeability is constant, then variation of the signal velocity will be dependent only on variation of the dielectric constant. In a transmission line, signal velocity is the reciprocal of the square root of the capacitance-inductance product, where inductance and capacitance are typically expressed as per-unit length.