The way in which the effect of the instrumental polarization of a spectrograph can distort the shape of the intensity profiles in sunspots is shown empirically. A spectral region around a magnetically sensitive line and a sunspot away from the disk center were chosen. The resulting limitations which arise when trying to derive physically meaningful results from distorted data are discussed. It was found that spectra of magnetic-sensitive lines in sunspots may be contaminated by the instrumental polarization of the spectrograph.