  We present the R-band polarimetric results towards two nebulae L1415 and
L1389 containing low luminosity stars. Aim of this study is to understand the
role played by magnetic fields in formation of low luminosity objects. Linear
polarization arise due to dichroism of the background starlight projected on
the cloud providing the plane-of-the sky magnetic field orientation. The
offsets between mean magnetic field directions obtained towards L1415 and L1389
and the projected outflow axes are found to be 35$^{\circ}$ and 12$^{\circ}$,
respectively. The offset between cloud minor axes and mean envelope magnetic
field direction in L1415 and L1389 are 50$^{\circ}$ and 87$^{\circ}$,
respectively. To estimate the magnetic field strength by using the updated
Chandrasekhar-Fermi relation, we obtained the $^{12}$CO(J=1-0) line velocity
dispersion value towards L1415 cloud using the TRAO single dish observations.
The values of B$_{pos}$ in L1415 and L1389 are found to be 28$~\mu$G and
149$~\mu$G using CF technique and 23$~\mu$G and 140$~\mu$G using structure
function analysis, respectively. The values of B$_{pos}$ in these clouds are
found to be consistent using both the techniques. By combining the present
results with those obtained from our previous study of magnetic fields in cores
with VeLLOs, we attempt to improve the sample of cores with low luminosity
protostars and bridge the gap between the understanding of importance of
magnetic fields in cores with VeLLOs and low luminosity protostars. The Results
of this work and that of our previous work show that the outflow directions are
aligned with envelope magnetic fields of the clouds.
