This paper is dedicated to the memory of Academician Il'ya Mikhailovich Frank (1908--1990). The papers of I.M. Frank for the period 1972--1974 concerning the optics of ultracold neutrons (UCN) are briefly reviewed and compared with later results obtained in this field. The basic stages of the development of a neutron microscope based on UCN are briefly described. The possibility of using neutron-optical methods for fundamental investigations with long-wavelength neutrons is discussed.