Aims:Off-the-limb observations with high spatial and spectral resolution will help us understand the physical properties of spicules in the solar chromosphere. Methods: Spectropolarimetric observations of spicules in the He i 10 830 Å multiplet were obtained with the Tenerife Infrared Polarimeter on the German Vacuum Tower Telescope at the Observatorio del Teide (Tenerife, Spain). The analysis shows the variation of the off-limb emission profiles as a function of the distance to the visible solar limb. The ratio between the intensities of the blue and the red components of this triplet (R=I_blue/I_red) is an observational signature of the optical thickness along the light path, which is related to the intensity of the coronal irradiation. Results: We present observations of the intensity profiles of spicules above a quiet Sun region. The observable R as a function of the distance to the visible limb is also given. We have compared our observational results to the intensity ratio obtained from detailed radiative transfer calculations in semi-empirical models of the solar atmosphere assuming spherical geometry. The agreement is purely qualitative. We argue that future models of the solar chromosphere and transition region should account for the observational constraints presented here.