Velocity of light in moving media, Sagnac formula and its application in optical gyroscopes

In 1913, the French physicist Georges Signac published some experimental results and properties which describe the effect of velocity of light on moving media name on his name called "Signac effect". In the Signac experiment a circular platform rotated uniformly around a vertical axis. In an interferometer mounted on the platform, two interfering light beams, reflected by four mirrors, propagated in opposite directions along a closed horizontal circuit defining a certain area A. The rotating system included also the luminous source and a detector (a photographic plate recording the interference fringes ). On the pictures obtained during clockwise and counterclockwise rotations the interference fringes were observed to be in different positions. This fringe displacement is strictly tied to the time delay with which a light beam reaches the detector with respect to the other one and turns out to depend on the disk angular velocity. Signac observed a shift of the interference fringes every time the rotation was modified. Considering his experiment conceptually similar to the Michelson Morley one, he informed the scientific community with his research papers.

Condition 1: Beam must travel a distance d = in time t₁ or d = in time t₂ for the opposite direction in the moving frame as measured in the rotating frame of a fixed observer.

Condition 2 : Space must contract in the direction, but d = 2πR for a circular path.

Here is the time difference known as Signac Time lag between inertial observer at rest and the center of the rotation. This is directly proportional to the angular velocity of rotation. This was an interesting and equally logical result of the Michelson Morley experiment is the negation of universal ether for light propagation in favor of a continuum specific to each frame of reference