Spectropolarimetric observations of spicules were carried out with the new optical setup of the Tenerife Infrared Polarimeter (TIP 2) at the VTT, showing the variation of the He I 10830Å multiplet off-limb emission profiles with increasing distance to the solar visible limb. The ratio between the intensities of the blue and the red components of this triplet (R = Iblue/Ired) is an observational signature of the optical thickness along the light path, which, at the same time, is proportional to the population of the lower (metastable) level that takes part in these transitions. Our observational results show a variation of R as a function of the distance to the limb. In agreement with recent theoretical results we conclude that R could be used as a diagnostic tool for downward UV coronal irradiance, which is believed to be responsible for the population of the metastable level of the He I 10830 Å triplet. We have compared our observational results with the ratio obtained from detailed radiative transfer calculations in semi-empirical models of the solar atmosphere (assuming spherical geometry) finding a fairly poor agreement. We argue that future models of the solar chromosphere and transition region should account for the observational constraints presented here.