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The pulsed radiation from the Crab pulsar consists of the main pulse (MP) and inter pulse (IP), as well as of the extra pulse components appearing at certain frequencies. It has been studied at many frequencies and contains unique information, which is not available for the majority of the pulsars. One of the mysteries of these data, found by Moffett and Hankins twenty years ago, is the shift of the IP at high radio frequencies compared to lower ones and return to its previous position in the more high-frequency optical and X-ray range. We propose the explanation of these mysterious changes with the frequency through reflection of radiation by relativistic positrons from the star surface. The positrons, which are accelerated towards the surface of the star by the inner gap electric field, radiate as "half-bare" particles. The spectral-angular properties of this radiation differ from those ones of the electron curvature radiation inside the gap. The magnetic field of the pulsar may include toroidal component that emerges on the surface of the star and affects on the discussed processes.