In a quasioptical approximation we develop a theory of an open cavity with a dielectric plate placed normally to the cavity axis. We find conditions under which some natural frequencies of the cavity are practically independent of the plate position in the cavity. From experimental measurements of one of these frequencies and with variation of the length of the cavity with and without the plate, with the same oscillation- mode structure, we determine the refractive index and plate thickness. Coincidence between the obtained (“design”) thickness and mechanically measured one is a correctness criterion for the results obtained.