I'm looking at the (local) intensity of an MC propagating wave in terms of the electric field and I found something pretty good: \begin{equation} \left|E\right|^2 = \frac{2I}{\epsilon_0 c}. \end{equation}
(The source https://www.rp-photonics.com/optical_intensity.html has something similar)
I would like to derive this result myself (it doesn't look too difficult), but I don't know where to start, nor could I find this in the optics book that I used for my undergraduate course on optics (Hecht).
Who knows the derivation and/or can give me a good hint on what material I could try to rederive this expression? I know the idea of multiplying energy density by wave velocity, and the expression for the wave velocity. What I don't know is how to derive \begin{equation} u = \frac12 \epsilon_0 n^2 \left|E\right|^2 \end{equation}
