# 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.