We present a method for predicting the geometric phase introduced by wave plates and a polarizer, wherein mathematical formulas to calculate the phase using the Mueller formalism are visualized as a triangle on the surface of the Poincare sphere. These constructions are used to describe a simple experiment with a birefringent medium in a Mach–Zehnder interferometer and polariscopic setup. A geometric radio frequency (RF) phase shifter for controlling the geometric phase introduced by the birefringent medium is also presented. The RF phase generated from orthogonally polarized light signals was shifted from 0 deg to 360 deg; this phase shift exhibited nonlinear characteristics. Thus, the proposed phase-shifter device improves phase control sensitivity in the partial region.