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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. Thus the wavelength of a 100 MHz electromagnetic (radio) wave is about: 3 × 10 8 m/s divided by 10 8 Hz = 3 m. The wavelength of visible light ranges from deep red, roughly 700 nm, to violet, roughly 400 nm (for ...
The standard Compton wavelength λ of a particle of mass is given by =, where h is the Planck constant and c is the speed of light. The corresponding frequency f is given by f = m c 2 h , {\displaystyle f={\frac {mc^{2}}{h}},} and the angular frequency ω is given by ω = m c 2 ℏ . {\displaystyle \omega ={\frac {mc^{2}}{\hbar }}.}
For example, for visible light, the refractive index of glass is typically around 1.5, meaning that light in glass travels at c / 1.5 ≈ 200 000 km/s (124 000 mi/s); the refractive index of air for visible light is about 1.0003, so the speed of light in air is about 90 km/s (56 mi/s) slower than c.
Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Wavelength: λ: General definition (allows for FM): = / For non-FM waves this reduces to:
Using two formulas from special relativity, one for the relativistic mass energy and one for the relativistic momentum = = = = allows the equations for de Broglie wavelength and frequency to be written as = = = =, where = | | is the velocity, the Lorentz factor, and the speed of light in vacuum.
This equation is known as the Planck relation. Additionally, using equation f = c/λ, = where E is the photon's energy; λ is the photon's wavelength; c is the speed of light in vacuum; h is the Planck constant; The photon energy at 1 Hz is equal to 6.626 070 15 × 10 −34 J, which is equal to 4.135 667 697 × 10 −15 eV.
The refractive index, , can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, and similarly the wavelength in that medium is λ = λ 0 /n, where λ 0 is the wavelength of that light in vacuum.
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.