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In a dispersive medium, the phase speed itself depends upon the frequency of the wave, making the relationship between wavelength and frequency nonlinear. In the case of electromagnetic radiation—such as light—in free space, the phase speed is the speed of light, about 3 × 10 8 m/s.
Longer-wavelength radiation such as visible light is nonionizing; the photons do not have sufficient energy to ionize atoms. Throughout most of the electromagnetic spectrum, spectroscopy can be used to separate waves of different frequencies, so that the intensity of the radiation can be measured as a function of frequency or wavelength ...
In such a theory, its speed would depend on its frequency, and the invariant speed c of special relativity would then be the upper limit of the speed of light in vacuum. [32] No variation of the speed of light with frequency has been observed in rigorous testing, putting stringent limits on the mass of the photon. [ 59 ]
As a wave, light is characterized by a velocity (the speed of light), wavelength, and frequency. As particles, light is a stream of photons . Each has an energy related to the frequency of the wave given by Planck's relation E = hf , where E is the energy of the photon, h is the Planck constant , 6.626 × 10 −34 J·s, and f is the frequency ...
The primary properties of light are intensity, propagation direction, frequency or wavelength spectrum, and polarization. Its speed in vacuum , 299 792 458 m/s , is one of the fundamental constants of nature. [ 6 ]
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 ]
Light waves of all frequencies travel at the same speed of light while matter wave velocity varies strongly with frequency. The relationship between frequency (proportional to energy) and wavenumber or velocity (proportional to momentum) is called a dispersion relation.
For example, a wavenumber in inverse centimeters can be converted to a frequency expressed in the unit gigahertz by multiplying by 29.979 2458 cm/ns (the speed of light, in centimeters per nanosecond); [5] conversely, an electromagnetic wave at 29.9792458 GHz has a wavelength of 1 cm in free space.