The absorption and fluorescence emission spectra of a newly synthesized laser grade coumarin dye, 1-((4-methoxyphenoxy) methyl)-3H-benzo[f]chromen-3-one (4-MPMBC), have been recorded in various solvents having different polarities. The spectrum peak was found to shift toward a higher wavelength with an increase in the solvent polarity. The dipole moments of the ground state (μg) and excited state (μe) were estimated using the Lippert, Bakshiev, and Kawski–Chamma–Viallet equations. The μe values were found to be greater than the μg values in all solvents, indicating that the dye is more polar in the excited state than in the ground state. The absorption maximum and emission maximum energies, ground- and excited-state dipole moments, and HOMO–LUMO energy gaps were estimated using Gaussian 16W. These have been compared with the experimental results. The estimated chemical hardness of the dye molecule indicates the soft nature in all of the solvents. The reactive centers such as nucleophilic and electrophilic sites were identified along with contour action using electrostatic potential three-dimensional map density functional theory analysis. The fluorescence quenching has been studied in solvents of varying polarities using aniline as a quencher. The quenching process was found to follow the Stern–Volmer equation and was studied by considering the role of diffusion. In all solvents, the probability of quenching per encounter (p) was found to be less than unity. The activation energy for diffusion and activation energy for quenching were estimated using the values of p.