A short-wavelength light-emitting element such as an ultraviolet light-emitting element or blue light-emitting element is arranged in a container which has a window with a window board formed of calcium fluoride crystals. Fluoride crystals are ones which contain either metal or metal halide, or both of them. In a production method of fluoride crystals in which the cavity of a crucible is filled with raw material powder and this crucible is heated in a vertical Bridgman furnace, a production method of fluoride crystals of the present invention is the one in which the shortest diameter of a cross section of the cavity of the crucible is small. In a crucible, whose cavity is filled with raw material powder, heated in a vertical Bridgman furnace to produce fluoride crystals, a crucible is the one in which the shortest diameter of a section of the cavity is small.