We consider the dynamics of a variable optical prism based on Pancharatnam phase. The device basics, using liquid crystals (LCs) as the electro-optical material, have been previously proposed. In this paper, we study the dynamics of discrete changes in the phase profile, and also continuous changes in the phase profile through acquired data and numerical modeling. We show that a design based on LCs whose dielectric anisotropy can change sign (as a function of frequency) allows continuous tuning with reasonable response times.