In this article, the growth kinetic and optical property of amorphous carbon (a-C) nanolayers deposited by ion beam sputtering deposition technique on glass substrates are investigated. The atomic force microscopy is used to measure the variation of surface roughness versus deposition time. According to the calculations, the roughness of thin films increases during the growth process as a fractal scaling law. The Hurst exponent (α) has a value higher than 0.5, and the growth exponent (β) changes in the range of 0.02 to 0.22. These fractal exponents predict that the growth process of amorphous carbon nanolayers obeys the rules of the WolfVillain model belonging to the Edwards-Wilkinson universality class, in which the relaxation and surface diffusion happen during the growth process. The results indicate that the optical band gap decreases by reducing the surface roughness, Hurst exponent and the correlation length during thin film growth which is the first observation of this trend.