deletions | additions       diff --git a/Let_s_describe_the_phenomenon__.tex b/Let_s_describe_the_phenomenon__.tex  index 6953d83..5bb6a34 100644  --- a/Let_s_describe_the_phenomenon__.tex  +++ b/Let_s_describe_the_phenomenon__.tex 
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Let's describe the phenomenon in a physical point of view.  The optical intensity $I_0$ of the laser beam is defined as $I_0=\frac{1}{S}\frac{d E}{dt}$, where $E$ is the beam energy and $S$ the beam surface. When the laser beam is emitted on the medium, it absorbed with an exponential decay along medium depth $z$: $I(z)=(1-R) \begin{equation}  I(z)=(1-R)  I_0 \exp(- \gamma z)$, z)  \label{eq:expontentialDecay}  \end{equation}  where $R$ is the reflection coefficient of the material (supposed negligible on a black mat material as the one used here) and $\gamma$ the absorption coefficient of the medium. The absorption coefficient $\gamma$ can be estimated in two ways: by measuring the fraction of light going through different thickness of the medium or by calculating the skin depth $\delta$, equal to $2 \gamma^{-1}$ (the factor 2 is due to the fact that $\delta$ is related to magnitude of the electrical field while $\gamma$ is related to the magnitude of the optical energy, which is the square of the electrical field magnitude). $\delta$ is equal to: \begin{equation}  \delta = \frac{1}{\sqrt{\pi \sigma \mu_r \mu_0 \nu}}  \label{eq:skinDepth}