Physical meaning of wavelength of a EM Wave The wavelength of a wave is defined as the spatial separation after which it repeats its shape. It is easy to visualize it for one dimension but if we consider a light wave/EM wave which is propagating in three dimensional space, how do we physically understand the spatial separation after which the wave repeats itself in this case?
 A: Suppose you shine a linearly polarized laser at the wall. Let's call the direction of laser propogation $\hat{z}$ and the direction of the electric field polarization $\hat{x}$. Then if you plot the $x$-component of the electric field vs. $z$, you will get a sine wave. The wavelength of the light is the wave length of the sine wave. So if one peak was at $z=1\mathrm{m}$ and the next peak was at $z=2\mathrm{m}$, then the wavelength $\lambda$ would be given by $\lambda = 2\mathrm{m} - 1\mathrm{m} = 1\mathrm{m}$.
A: The wavelength is not defined as the length after which the waves repeats itself: that is only a pictorial representation that works in one dimension for simple one component waves but it is not valid in general. Instead, given any solution of a wave equation represented as Fourier transform
$$
\psi(\textbf{x},t)=\int d^3k\,d\omega\,\tilde{c}(\textbf{k},\omega)\,\textrm{e}^{-i(\textbf{k}\cdot\textbf{x} - \omega t)}
$$
the wavelength of each Fourier component $\tilde{c}(\textbf{k})$ is defined as $\lambda=2\pi/|\textbf{k}|$. This reduces to the standard pictorial representation in one dimension if you take only the components in the integral giving rise to either the sine or the cosine function.
