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When EM waves travel through a material with refraction index n, ist the formula $\lambda = \frac{c}{n \cdot f}$ correct? c is the speed of light in vacuum and f the frequency of the wave. Thank you!

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n is called the refractive index and can be defined as follow : $$ n = \frac{c}{v} $$ With $v$ being the wave's phase velocity.

The "true" relation would be : $$ \lambda = \frac{v}{f} $$ Which according the definition of $n$ gives $$ \lambda = \frac{c}{nf} $$

$n$ is also defined by: $$ n = \sqrt{\epsilon_r} = \sqrt{\frac{\epsilon}{\epsilon_0}} $$ With $\epsilon_0$, $\epsilon$ and $\epsilon_r$ being respectively the vacuum's dielectric permittivity, the material's dielectric permittivity, and the material's relative permittivity.

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