A microliquid prism is a microchannel filled with two immiscible liquids, whose interface acts as a refractive surface. To steer a light beam that constructs optical images, the interface profile or the contact angle is modulated through electrowetting on a dielectric. Accurate, yet agile actuation of the liquid prism critically depends on the understanding of dynamics of the fluid interface. Here we fabricate liquid prisms, visualize the shape evolution of the interface, and theoretically model its dynamics. By comparing the magnitude of capillary forces to those of viscous, inertial and hydrostatic forces, we find that the meniscus motion within submillimetric channels is dominated by the capillary effect. The theoretical predictions for microscale meniscus dynamics are shown to agree well with the experimental measurements. We then discuss the formation of waves in millimetric liquid prisms, which may significantly limit fast and reliable operation of the optofluidic device.