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docs/en/physics/electromagnetism/optics/electromagnetic-waves.md

@@ -47,12 +47,16 @@ The above proposition gives an example of a light wave, but note that there are
 
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 > *Law*: the electric field $\mathbf{E}$ and the magnetic field $\mathbf{B}$ in a electromagnetic wave are orthogonal to each other; $\langle \mathbf{E}, \mathbf{B} \rangle = 0$. 
 
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 > *Corollary*: it follows from the above law that the magnitude of the electric and magnetic fields $E, B: U \to \mathbb{R}$ in a electromagnetic wave are related by 
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@@ -79,6 +83,8 @@ The above proposition gives an example of a light wave, but note that there are
 
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 > *Definition*: the time average of the magnitude of $\mathbf{S}$ is called the irradiance. 
 
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docs/en/physics/electromagnetism/optics/waves.md

@@ -26,6 +26,10 @@ The derivation of the wave equation can be obtained in section...
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 > for all $(x,t) \in \mathbb{R}^2$. With $k = \frac{2\pi}{\lambda}$ the wavenumber, $\omega = \frac{2\pi}{T}$ the angular frequency and $v = \frac{\lambda}{T}$ the wave speed. 
 
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 A right travelling harmonic wave $\Psi: \mathbb{R}^2 \to \mathbb{R}$ can also be represented in the complex plane given by
 
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@@ -42,6 +46,11 @@ for all $(x,t) \in \mathbb{R}^2$.
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 > for all $(\mathbf{x},t) \in \mathbb{R}^4$. 
 
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 We may formulate various solutions $\Psi: \mathbb{R}^4 \to \mathbb{R}$ for this wave equation. 
 
 The first solution may be the plane wave that follows cartesian symmetry and can therefore best be described in a cartesian coordinate system $\mathbf{v}(x,y,z)$. The solution is given by