The frequency of the plasma with the c axis polarization in the cuprate superconductors is extremely low and it is lower than the superconducting energy gap in some cuprate. Electromagnetic phenomena caused by the excitation of the plasma are theoretically studied. The light passing through a film of the cuprate superconductor strongly interacts with the transverse component of the plasma. The interference effect of the plasma waves reflected at both sides of the film causes the oscillatory frequency dependence of the reflectivity and transmissivity. When vortices are introduced by an external magnetic field, the vortex motion and the gapless excitation inside the vortex normal cores make the reflectivity and transmissivity strongly field dependent. When a static voltage is applied to a Josephson junction of the cuprate superconductor, the plasma is excited by the ac Josephson effect and the excited plasma decays by emitting light. The excited plasma brings about an anomalous current-voltage characteristics in a weak magnetic field.