We demonstrate an approach that allows for measurement of the real part of the refractive index (RI) and the thickness of the coating deposited on the cylindrical surface of a thinned optical fiber using a tin dioxide (SnO2) film as an example. While the layer is being synthesized, lossy mode resonances (LMRs) are observed in the transmission spectra of the fiber light guide at any particular wavelength at regular intervals. It is shown that there are at least two functions by which the RI of a film can be calculated from the obtained spectra.