This thesis describes a fundamental study of the miscibility and the nature of the interface between components of core-shell polymer blends using the technique of Fluorescence Resonance Energy Transfer (FRET) coupled with data analysis that involves Monte-Carlo simulations. Our aim in this study was to develop a fundamental methodology to quantitatively determine the width of the interface between the two components in binary polymer blends. At the current state of the art, data analysis of FRET experiments requires translational symmetry. In the system under study, uniform core-shell structures satisfy this criterion. Thus, in this work our focus was directed toward the study of a blend system with a core-shell structure. For this FRET study, I have identified a number of potential donor and acceptor dye pairs that fluoresce in the visible range of the spectrum and can be chemically attached to polymers. Among them, I selected, as the donor and the acceptor, a pair of naphthalimide dyes that have not previously been used for FRET experiments. Model experiments showed that while the fluorescence decay profile of the donor chromophore was exponential in solution, it was not exponential in polystyrene (PS) or poly(methyl methacrylate) (PMMA) films. Thus, I carried out refinements to existing FRET theory to interpret the data generated by using these dyes. Also, I derived a new model to predict the fluorescence intensity of non-exponential decaying donor dyes in core-shell systems. I selected a model system composed of a PS core surrounded by a PMMA shell. The PS core particles were prepared by miniemulsion polymerization to obtain cross-linked PS particles with a narrow size distribution. Seeded emulsion polymerization under starved-fed condition was employed to synthesize monodisperse dye-labeled core-shell particles. The extent of miscibility and the nature of interface between the core and the shell polymers were retrieved from a combined study by Monte-Carlo simu.