Abstract: In the measuring instrument, a light beam generated by a laser (1) is split into two component beams (L(CW), L(CCW)) which travel along a coiled optical waveguide (7) in opposite directions. After traversing the optical waveguide, the two component beams are superimposed on each other (5) and directed to an optical/electrical transducer (8). One of the two component beams (L(CW)) is frequency-modulated in a Bragg cell (6) before entering the optical waveguide (7), switchover being effected between two modulation frequencies (f1, f2) at a given frequency (F.sub.S). The modulation frequencies are chosen so that, after traversal of the optical waveguide (7), the phase differences (.phi..sub.B1, .phi..sub.B2) between the two component beams (if the rotation rate .OMEGA.=0) are .pi./2 and 3.pi./2 or even integral multiples thereof. In case of rotation, the phase difference (.phi..sub.S) caused by the Sagnac effect is superimposed on these phase differences.