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In X-ray spectra of several active galactic nuclei and Galactic black holebinaries a broad relativistically smeared iron line is observed. This featurearises by fluorescence when the accretion disc is illuminated by hot coronaabove it. Due to central location of the corona the illumination and thus alsothe line emission decrease with radius. It was reported in the literature thatthis decrease is very steep in some of the sources, suggesting a highly compactcorona.  We revisit the lamp-post setup in which the corona is positioned on the axisabove the rotating black hole and investigate to what extent the steepemissivity can be explained by this scenario. We show the contributions of therelativistic effects to the disc illumination by the primary source - energyshift, light bending and aberration. The lamp-post radial illumination patternis compared to the widely used radial broken power-law emissivity profile. Wefind that very steep emissivities require the primary illuminating source to bepositioned very near the black hole horizon and/or the spectral power-law indexof the primary emission to be very high. The broken power-law approximation ofthe illumination can be safely used when the primary source is located atlarger heights. However, for low heights the lamp-post illuminationconsiderably differs from this approximation.  We also show the variations of the iron line local flux over the disc due tothe flux dependence on incident and emission angles. The former depends mainlyon the height of the primary source while the latter depends on the inclinationangle of the observer. Thus the strength of the line varies substantiallyacross the disc. This effect may contribute to the observed steeper emissivity.

An XSPEC model to explore spectral features from black-hole sources - II. The relativistic iron line in the lamp-post geometry