The invention provides a fiber-optic sensing system for measuring a curvature in a small and elongated cavity of an object. The system includes a light source, an optical fiber and a light signal reflecting device disposed at a distal end of the optical fiber. The optical source emits a light signal into the optical fiber. The distal section of the optical fiber is inserted into the cavity of the object which curvature is to be measured. The curvature of the cavity bends the distal section of the optical fiber so that attenuation of light signal transmitting through the distal section occurs. This attenuated signal is reflected by a reflecting device and coupled into a measuring device. Thereby the curvature is deduced in accordance with the amount of energy attenuation in the reflected light signal.