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Each medium is characterized by its own propagation speed that gives rise to a characteristic refractive index. Since speed can depend on the frequency of light, the index of refraction is also a function of this.
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Given that the photon frequency ($\nu$) is the inverse of the period ($T$):
$\nu=\displaystyle\frac{1}{T}$
this means that the speed of Light ($c$) is equal to the distance traveled in one oscillation, which is ERROR:8439, divided by the elapsed time, which corresponds to the period:
$c=\displaystyle\frac{\lambda}{T}$
In other words, the following relationship holds:
The energy of a wave or particle (photon) of light is given by
When this energy propagates from one medium, for example, a vacuum with a speed of light $c$, to another medium with a speed of light $c_m$, it is concluded that the frequency of light remains unchanged. However, this implies that, since the speed of light is equal to the product of frequency and wavelength, as expressed in the equation
the wavelength must change as it transitions between mediums.
Therefore, if we have a wavelength of light in one medium $\lambda_m$ and in a vacuum $\lambda$, the refractive index can be defined as
and can be expressed as
$n=\displaystyle\frac{c}{c_m}=\displaystyle\frac{\lambda\nu}{\lambda_m\nu}=\displaystyle\frac{\lambda}{\lambda_m}$
In other words,
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The photon is described as a wave, and the photon frequency ($\nu$) is related to ERROR:8439 through the speed of Light ($c$), according to the following formula:
This formula corresponds to the mechanical relationship that states the wave speed is equal to the wavelength (distance traveled) divided by the oscillation period, or inversely proportional to the frequency (the inverse of the period).
The refractive index, denoted as $n$, is defined as the ratio of the speed of light in a vacuum, denoted as $c$, to the speed of light in the medium, denoted as $c_m$:
If $n$ is the refractive index in a medium and $\lambda$ is the wavelength in a vacuum, then when propagating in the medium, the wavelength $\lambda_m$ will be
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