Resonance frequency shift in a cavity with a thin conducting film near a conducting wall

We show that a very thin conducting film (whose thickness can be much smaller than the skin depth), placed nearby a wall of an electromagnetic cavity, can produce the same shift of the resonance frequency as a bulk conducting slab, provided the displacement of the film from the wall is much bigger than the skin depth. We derive a simple analytical formula for the frequency shift and compare it with exact numerical calculations and experimental data.