Abstract. The relative role played by the magnetic field and the turbulence in cloud formation and evolution and in different stages of star formation is a matter of serious study. By using linear polarization measurements in optical wavelengths of stars that are located behind the clouds, one can map the plane-of-sky component of magnetic field. Here we present the preliminary results of the linear polarimetry of background stars projected on three clouds, namely, IRAM 04191+1522 (R band), L1521F (V band) and L1014 (R band). These clouds, previously classified as starless, are found to harbour very low luminosity objects (VeLLOs, L ≤ 0.1 L_⊙) detected during observations with Spitzer Space telescope (SST). A protostar located on the stellar/substellar boundary (M=0.08M_⊙) would have an accretion luminosity of L∼ 1.6L_⊙, assuming a spherical mass accretion predicted by the standard model onto a protostellar object of typical radius R∼ 3 R_⊙. VeLLOs, with luminosities more than an order of magnitude lower than this, are difficult to understand in the context of standard model of star formation.

Key words:ISM: magnetic fields -- polarization -- star: formation