An elementary proof of the geometrical dependence of the Sagnac effect

We offer an elementary proof, within a classical model, that the beat frequency produced in an active optical Sagnac interferometer, in which clockwise (CW) and counterclockwise (CCW) waves are mixed, is proportional to its vector area A divided by its perimeter P. We aim to fill a gap in the literature, since alternative proofs are usually incomplete or rather more complicated. Our observations in various large ring laser interferometers support this A/P dependence and allow the observed Sagnac frequencies from Earth rotation to be predicted to very high accuracy.