# Fresnel's Equations Range of Validity

Do Fresnel's equations ever break down at extremely small length scales?

I am wondering if I can apply Fresnel's equations to a very thin film (~10-20nm) at an interface with air with a free-space wavelength in the micron range. I know Fresnel's equations are derived from Maxwell's equations and material properties, and I'm not aware of cases where these equations aren't valid so long as non-idealities of the materials are taken into account and the particle nature of light isn't important.

The Fresnel equations are based on the plane-wave solutions of the electromagnetic field. As such, there is nothing that forces them to break down for films that are thinner than the wavelength (and, indeed, they are essential in describing anti-reflectant coatings that are films of about $\frac14$-wavelength thickness.

On the other hand, you do need the medium to be describable as a bulk dielectric, and you need the interface to be sharp. If you have some smooth degrading of the medium's density at the interface, or your dielectric has some funky behaviour like e.g. the polarizability increasing at the boundary because of surface effects, and those things happen on length scales that become comparable with the thickness of the film, then those would certainly impact the applicability of the Fresnel formalism.