A reflective intensity-modulation-based fiber optic position sensor is studied. The sensor consists of input and output channels attached with graded-index (GRIN) lenses. The input channel launches a collimated probe beam onto a sample, and then the output channel collects the light reflected and scattered from the sample. Light power from the output channel directly depends on the distance between the sensor head and the sample (the proximity), which defines a modulation function to characterize the sensor. For practical purposes, effects of sample reflectivity on sensor response are discussed for the cases of specularly reflective and Lambertian diffusive samples. Effects of sample rotations are also studied.