The current research is a spectroscopic study of Coumarin 334 dissolved in methanol. The range of concentrations of the prepared stock solution was (3.39x10^-9 to 2.03x10^-8) M. Some optical characteristics of this dye were investigated such as absorbance and transmission spectra, absorption coefficient, refractive and extinction coefficients, oscillation and dispersion energies, and energy band gap. The absorbance spectra were recorded at 452 nm using Broad Band Cavity Enhanced Absorption Spectroscopy (BBCEAS) which depends on increasing the path length of the traveling light from the source to the detector. The minimum absorbance amount was 0.07 with a low concentration of 3.39x10^-9 M. As a result, the other optical properties were calculated on the basis of the lowest values of absorbance. The energy band gap, which is important to detect the electronic band structure of the material,  was determined; it was found to be equal to ~2.55 eV. The low values of the concentration made less collision between the molecules in the materials and the incident light. This led to a reduction in the background noise and in the percentages of losses. Furthermore, the dispersion and single oscillator energies, which help to calculate the average strength of the inter-band optical transitions and to prepare the quantifiable information about the band structure of the material, were calculated to reduce with the increasing concentrations. The refractive and extinction coefficients were determined because they are considered important factors for the optical materials and found to increase with the increasing concentrations. As a result, the study of the optical behavior of Coumarin 334 highlighted the promising materials for photonics applications at very low concentrations. All these properties are considered the main factors to determine the usefulness of the materials in advanced applications and to develop the performance of the devices which depend on the optical characteristics.