Cu films of different thickness were deposited on K9 glass using ion beam sputtering. The reflectance and transmittance of Copper films in the wavelength range from 310 nm to 1300 nm have been measured by Lambda-900 spectrophotometer. Relationships between reflectance,transmittance,absorptance and thickness of Cu films in the wavelength selected 310,350,400,430,550,632,800,1200 nm have been discussed. The optical constants of Cu films have also been discussed. The results show that the optical properties of Cu films have obvious size effect. There is a point of intersection,which is located in the relationship curves of between reflectance,transmittance and thickness of Cu films at wavelength 550 nm. The corresponding thickness of this point of intersection can be thought of as the minimal continuous thickness of the growth of metallic films from discontinuous to continuous. According to this characteristic criterion,the minimal continuous thickness of Cu films prepared by ion beam sputtering is 33 nm. The topography images of Cu films near the minimal continuous thickness were observed by using atomic force microscopy (AFM).