gold could already include some effect of water. Then the agreement between forces measured and predicted theoretically for pure gold becomes questionable. Therefore, the first question to answer is how well we may know the dielectric function of gold samples from measurements in ambient conditions? This question has also an independent interest for the community dealing with the Casimir effect. Moreover, one could try to extract information on thickness of water films from optical measurements. These problems are closely related and we will analyze them in this subsection.

The ellipsometry can give the “pseudodielectric” function of the investigated material as $$\label{ps_diel}
    \langle \varepsilon\rangle=\sin^2\vartheta\left[1+\tan^2\vartheta
    \left(\frac{1-\rho}{1+\rho}\right)^2\right],$$ where $\vartheta$ is the angle of incidence, and $\rho$ is the directly measured complex ratio of the reflection coefficients $\rho=r_p/r_s$. If the investigated material is a pure gold film, then $\langle \varepsilon\rangle$ as calculated from (\[ps\_diel\]) will correspond to the dielectric function of $Au$ and the reflection coefficients $r_{s,p}$ will coincide with that in (\[r\_def\]).

If there is a water layer of thickness $h$ on top of gold film, then the reflection coefficients entering in (\[ps\_diel\]) will be different. Let us enumerate the media air-water-gold by increasing indexes 0-1-2. Then for both polarizations we have $$\label{r_multi}
    