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A nonstationary electromagnetic radiation generated by a point source is considered. This source is placed near a plane interface separating a stationary medium and time-varying medium. It was shown that the presence of a plane boundary when a medium permittivity changes in time is essential for a field transformation. For example, it leads to a replacement of a convergence point of secondary spherical waves to the mirror symmetrical point. The field in this point is of a finite value in distinction of an unbounded medium.