Position 1: angle d L1A arm (deg.) Path L1B/L2B Lorentz contraction ( gLC ) Path L1A/L2A Lorentz contraction ( gLC ) velocity of local frame (m/s) Rotating Triangle Interferometer: L1 Length (m) SQRT(1-v^2/(c^2)) SQRT(1-v^2/(c^2)) angle d L1 arm (deg.) Refractive index (n) of arms L2 Length (m) Avg Time Dilation factor in v frame ( gt ) Path L1/L2 Lorentz contraction ( gLC ) X X Source Detector angle d L1B arm (deg.) SQRT(1-v^2/(c^2)) SQRT(1-v^2/(c^2)) 1 Path L1A Parallel: Path L1B Parallel: L1   C': 1/(n/c+v/c^2 * cosd +v^2n/2c^3(1+cos^2d)) Total Newtonian Time t Local time Dilated t'F (sec)  radial path t'F (sec) radial path t'F (sec) circumference path t' average (sec) t' average (sec) C'F (m/s) C'F (m/s) C'R (m/s) C' average (m/s) C' average (m/s) Path L2A Parallel: Path L2B Parallel: L2  C': 1/(n/c+v/c^2 * cosd +v^2n/2c^3(1+cos^2d)) Total Newtonian Time t Local time Dilated t'F (sec) t'F (sec) t'F (sec) t' average (sec) t' average (sec) C'F (m/s) C'F (m/s) C'R (m/s) C' average (m/s) C' average (m/s) Position 2: angle d L1A arm (deg.) Path L1B/L2B Lorentz contraction ( gLC ) Path L1A/L2A Lorentz contraction ( gLC ) velocity of local frame (m/s) Position 1 Length c/n L1 Length (m) SQRT(1-v^2/(c^2)) SQRT(1-v^2/(c^2)) m angle d L1 arm (deg.) Refractive index (n) of arms L2 Length (m) Avg Time Dilation factor in v frame ( gt ) Path L1/L2 Lorentz contraction ( gLC ) Position 2 Length angle d L1B arm (deg.) SQRT(1-v^2/(c^2)) SQRT(1-v^2/(c^2)) Light speed C (m/s) m Path L1 Parallel: Path L1 Parallel: C': 1/(n/c+v/c^2 * cosd +v^2n/2c^3(1+cos^2d)) Total Newtonian Time t Local time Dilated Rotation velocity t'F (sec) radial path t'F (sec) radial path t'F (sec) circumference path t' average (sec) t' average (sec) m/s Angle Position 1 C'F (m/s) C'F (m/s) C'R (m/s) C' average (m/s) C' average (m/s) o Path L2 Parallel: Path L2 Parallel: C': 1/(n/c+v/c^2 * cosd +v^2n/2c^3(1+cos^2d)) Total Newtonian Time t Local time Dilated t'F (sec) t'F (sec) t'F (sec) t' average (sec) t' average (sec) Angle Position 2 o C'F (m/s) C'F (m/s) C'R (m/s) C' average (m/s) C' average (m/s) Time Diff. Position 1 vs 2: Fringe Shift at Det. Pos. 1 vs 2 Angular velocity Length overall (m): time difference (Sagnac Effect) time difference Position 1 (sec) time difference at Position 2 (sec) Note: The source and detector are at the origin (0,0) on the graph. Motion is right to left. Radius Area fringe shift (Sagnac Effect) Fringe Diff forward/Rev.  (l) Fringe Diff Forward/Rev. (l) Light emitted by the source travels clockwise/counterclockwise around the triangle. The returning beams interfere at the detector forming a fringe pattern.