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We grew nano-crystalline SnO<sub>2</sub> thin films on Si substrates by using RF magnetron sputtering deposition method. We examined the microstructure of the SnO<sub>2</sub> thin films via X-ray diffraction (XRD) and the optical properties of the SnO<sub>2</sub> thin films via photoluminescence (PL) spectroscopy and spectroscopic ellipsometry. We obtained the dielectric functions (ε = ε<sub>1</sub> + <i>i</i>ε<sub>2</sub>) of the SnO<sub>2</sub> thin films in the visible to deep ultraviolet spectral range, as well as the anisotropic dielectric functions of the bulk SnO<sub>2</sub> single crystal. The band edge blue shift and the larger peak maximum of ε<sub>2z</sub> compared to those of ε<sub>2x</sub>, in the directions parallel and perpendicular to the optical c-axis, respectively, are consistent with calculations found in the literature. We estimated the critical point energies by using the second derivatives of the dielectric functions with respect to energy, and the results matched well with the calculated band structures in the literature. We also found critical point energies in the experimental data which were forbidden by selection rules in the calculations. The PL study of the SnO<sub>2</sub> thin films and bulk single crystals showed similar PL peaks associated with the band gap energy, suggesting that even the RT-grown thin film contained a very small number of crystalline nanograins even though the XRD spectra did not show any crystalline peaks.