Regularities of variation of output signal U of one reflection fiber optopair dependent on the distance h between active fiber tips and light reflecting body-mirror (U-h characteristics) and on the angle 2θ between the FAT axes, the distance between FAT being minimal (b = bmin), have been explored by modelling and experimentally. The parameters of U-h characteristics have been established: maximal sensitivity Smax(h), localization and values of maxima and inflection points (+,−) of a function U(h), length of interval ∆h in which the output signal U(h) is linear (98 % of sensitivity maxima), as well as dependences of these parameters on the angle θ and distance h. It has been shown that the experimental results are well described by the formulas improved by the authors previously. It has been demonstrated that reflection fiber optopair sensitivity Smax to displacement considerably increases with an increase of the angle θ. It has been defined that, with an increase of the angle θ up to 20°, sensitivity increases up to 30 times when active fiber tips axes are almost parallel and the diameter of the fiber core is 100 µm, and 125 µm with cladding. Apart from that, Smax increases almost exponentially up to θ = 20°. A drawback of such an RFP is that with an increase of the angle θ, the size of the sensor head also increases. However, due to their considerably increased sensitivity, they can be and are wide used.