We present the results of a theoretical numerical analysis of transmission characteristics of a fiber optic refractometric transducer with a hemispherical glass detection element. In this transducer, the internal reflection of light from the element's spherical surface depends on the refractive index of the surrounding medium. We examine the effects of the transducer's geometrical and optical parameters and its refractive index on the transmission function, its nonlinearity, and the transducer's sensitivity to the refractive index of the surrounding medium. We show that through a proper choice of the transducer's material and geometrical parameters, it is possible to obtain a transmission function of any necessary span over a wide interval of the refractive index of the surrounding medium (from n = 1.0 to 1.7), and to modify the form of the transmission function from a linear one to a steplike one in virtually the same device. This permits us to use the proposed transducer for two contrasting applications: assessing the refractive index, and discriminating between two liquids or between air and a liquid, as in the detection of liquids, level measurement, etc. In addition, it is possible to adjust the transducer input range to the refractive index of a particular fluid (or fluids) of interest.