The optical properties of Rhodamine 6G (R6G) dye in acetone solution were studied at different concentrations and thickness using Nd:YAG laser at the wavelength of 532 nm. The optical measurements were characterized by measuring the intensity of the medium using the Eclipsing Z-scan (EZ-scan) method. The samples in open aperture EZ-scan showed two-photon absorption. For the closed aperture, the dye exhibited a positive nonlinearity for all concentrations but showed negative (defocusing) nonlinearity at different thickness. The values of n2, β and |χ(3)| vary with the concentration and the thickness of the samples. Optical limiting characteristics of the dye at various concentrations and thickness in solution were studied.