Some advanced fiber-optic amplitude modulated reflection displacement sensors and refractive index sensors have been developed. An improved three-fiber displacement sensor has been investigated as a refractive index sensor by computer simulations in a large interval of displacement. Some new regularities have been revealed. A reflection fiber-optic displacement sensor of novel configuration, consisting of double optical-pair fibers with a definite angle between the measuring tips of fibers in the pairs has been proposed, designed, and experimentally investigated to indicate and measure the displacement and refractive index of gas and liquid water solutions. The proposed displacement sensor and refractive index sensor configuration improves the measuring sensitivity in comparison with the known measuring methods. The refractive index sensor sensitivity Snsub = 4 × 10−7 RIU/mV was achieved. The displacement sensor sensitivity is Ssub = 1702 mV/µm in air (n = 1.00027).