  The surface of a polar liquid presents a special environment for the
solvation and organization of charged solutes, which differ from bulk behaviors
in important ways. These differences have motivated many attempts to understand
electrostatic response at aqueous interfaces in terms of a spatially varying
dielectric permittivity, typically concluding that the dielectric constant of
interfacial water is significantly lower than in the bulk liquid. Such
analyses, however, are complicated by the potentially nonlocal nature of
dielectric response over the short length scales of interfacial heterogeneity.
Here we circumvent this problem for thin water films by adopting a
thermodynamic approach. Using molecular simulations, we calculate the solvent's
contribution to the reversible work of charging a parallel plate capacitor. We
find good agreement with a simple dielectric continuum model that assumes bulk
dielectric permittivity all the way up to the liquid's boundary, even for very
thin ($\sim 1$ nm) films. This comparison requires careful attention to the
placement of dielectric boundaries between liquid and vapor, which also
resolves apparent discrepancies with dielectric imaging experiments.
