Most metal films grow discontinuously in the early stages of the deposition. However, the optical behavior of discontinuous metal films is not yet well understood. We observed the growth process of Ag films on a Si substrate covered with a natural oxide layer using an in situ ultra-high vacuum spectroscopic ellipsometer over the spectral range from 260 nm to 860 nm. The growth process of the film was analyzed by means of an effective medium theory, which takes into account the discontinuous structure of the film. The analysis of the Psi-Delta trajectory of the Ag film suggests that surface roughening occurs in the growth process.