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The dependence of optical coefficients of ultrathin copper films 2-30 nm thick on the substrate thickness has been studied. Films were fabricated on quartz substrates 4 mm thick, and the thickness of the substrates (6 and 8 mm) was varied by tightly pressing clean substrates with thicknesses of 2 and 4 mm to a 4 mm substrate with a film. The measurements were carried out in a waveguide in the frequency range 8.5-12.5 GHz in the TE10 mode for two film orientations with respect to direction of the incident wave. The dependences of the optical coefficients measured when the wave was incident from the side of the film and from the side of the substrate differ significantly. It is shown that the effect of anomalously high absorption of waves (more than 77%) by copper films no thicker than 10 nm is observed in a wide frequency band. The maximum absorption (77.5%) was obtained at frequency of 8.5 GHz when a wave was incident on a film 8.6 nm thick from the side of a 6-mm substrate. The effect of extremely low reflection (0.06%) was recorded for the first time when a wave of frequency 11.54 GHz was incident on a film 7.9 nm thick from the side of a 4-mm substrate. It is shown that the frequency range where the effect of minimal reflection was observed exceeds the antireflection band of a dielectric plate with half-wave resonance. Keywords: ultrathin cooper films, quartz substrate, optical coefficients, waveguide measurements, microwave frequency range.