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Optical dielectric constants are critical to modeling the electronic and optical properties of materials. Silver, as a noble metal with low loss, has been extensively investigated. The recently developed epitaxial growths of single crystalline Ag on dielectric substrates have prompted efforts to characterize their intrinsic optical dielectric function. In this paper, we report spectral ellipsometry measurements and analysis of a thick, epitaxially-grown, single-crystalline Ag film. We focus on the range of 0.18 – 1.0 eV or 1.24 – 7 µm, an energy and wavelength range that has not been examined previously using epitaxial films. We compare the extracted dielectric constants and the predicted optical performances with previous measurements. The loss is appreciably lower than the widely quoted Palik’s optical constants (i.e., up to a factor of 2) in the infrared frequency range. The improved knowledge of fundamental optical properties of the high-quality epitaxial Ag film will have a broad impact on simulations and practical applications based on Ag in the long wavelength range.