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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 ]
Two of these equations predicted the possibility and behavior of waves in the field. Analyzing the speed of these theoretical waves, Maxwell realized that they must travel at a speed that was about the known speed of light. This startling coincidence in value led Maxwell to make the inference that light itself is a type of electromagnetic wave.
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 ...
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.
The speed of light in vacuum is defined to be exactly 299 792 458 m/s (approximately 186,282 miles per second). The fixed value of the speed of light in SI units results from the fact that the metre is now defined in terms of the speed of light. All forms of electromagnetic radiation move at exactly this same speed in vacuum.
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.
Figure 1. A source of light waves moving to the right, relative to observers, with velocity 0.7c.The frequency is higher for observers on the right, and lower for observers on the left.
In the context of electromagnetics and optics, the frequency is some function ω(k) of the wave number, so in general, the phase velocity and the group velocity depend on specific medium and frequency. The ratio between the speed of light c and the phase velocity v p is known as the refractive index, n = c / v p = ck / ω.