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Frequency and Wavelength of Photon
Equation
A photon is described as a wave, and its frequency $
u$ is related to its wavelength $\lambda$ through the speed of light $c$, according to the following formula:
 $ c = \nu \lambda $ |
Since frequency is the reciprocal of the time for one oscillation:
$\nu=\displaystyle\frac{1}{T}$
this means that the speed of light is equal to the distance traveled in one oscillation, which is the wavelength, divided by the time taken, which is the period:
$c=\displaystyle\frac{\lambda}{T}$
In other words:
| $ c = \nu \lambda $ |
This formula corresponds to the mechanical relationship that velocity is equal to the distance traveled (wavelength) divided by the time elapsed (frequency, which is the reciprocal of the period).
ID:(3953, 0)
Refraction Index
Equation
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 $c_m$:
| $ n =\displaystyle\frac{ c }{ v }$ |
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Refractive index and wavelength
Equation
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
| $ n =\displaystyle\frac{ \lambda }{ \lambda_m }$ |
The energy of a wave or particle (photon) of light is given by
| $ E = h \nu $ |
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
| $ c = \nu \lambda $ |
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
| $ n =\displaystyle\frac{ c }{ v }$ |
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,
| $ n =\displaystyle\frac{ \lambda }{ \lambda_m }$ |
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