The behavior of the power efficiency, Peff, of an optical fiber with a thin-film source distributed in the core/cladding interlace is analyzed. The expressions derived make use of the exact field solution of a cylindrical fiber, whereas previous work has made use of the weakly guiding approximation. Although more complicated and harder to interpret, the formulas presented allow the analysis of the power injection efficiency of fibers with arbitrary differences in indices of refraction. The results obtained are relevant to the design of more efficient optical fiber fluorosensors. In this work, some results using the weakly guiding approximation were confirmed. However, in contrast to the weakly guiding work, we have found that Peft does not always increase with the V number. It was found that Peff always increases with the difference in the indices of refraction, ncore - nclad, and varies only slightly with the wavelength, λ, and the fiber core radius, a. Finally, by varying a and λ in such a way as to make their ratio, a/λ, constant, it was found that Peff is also constant. This indicates that a/λ is a new independent variable.