$F_{\rm Cas}$ and a binding energy $E_{\rm Cas}$. Remarquably, they depend only on geometrical quantities, the area $A$ of the mirrors and their distance $L$ ($A\gg L^{2}$), and fundamental constants, the Planck constant $\hbar$ and the speed of light $c$.

Imperfect reflection {#sec:3}
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Experiments are performed with real metallic mirrors which good reflectors only at frequencies below their plasma frequency $\omega_{\rm P}$ which depends on the properties of the conduction electrons in the metal. The effect of imperfect reflection on the Casimir force and energy has been recognized long time ago [@Lifshitz56; @Schwinger78] though it has been described with good accuracy only recently [@Lamoreaux99; @Lambrecht00; @KlimPRA00]. We recall below the scattering theory of the Casimir force which has been developed and used to this aim [@Jaekel91; @GenetPRA03; @LambrechtNJP06].

We begin with perfectly plane and parallel mirrors, separated by a distance $L$. The two mirrors form a Fabry-Perot cavity and the fluctuations of the intracavity fields propagating back and forth along the cavity axis can be calculated in terms of the fluctuations of the incoming free-space fields. The field modes are characterized by their frequency $\omega$, transverse wavevector ${\bf k}$ with components $k_{x},k_{y}$ in the plane of the mirrors, and 