  Bright-rimmed clouds form on the edges of H II regions affected by the high
energy radiation from a central ionizing source. The UV radiation from the
ionizing source results in compression and ionization causing either cloud
disruption or further star formation. In this work, we present R-band
polarization measurements towards four bright-rimmed clouds, IC1396A, BRC 37,
BRC 38, and BRC 39, located in the different directions of the H II region,
Sh2-131, in order to map magnetic fields (B-fields) in the plane of the sky.
These BRCs are illuminated by the O star HD206267 and present a range of
projected on sky geometries. This provides an opportunity to understand the
magnetized evolution of BRCs. The B-field geometries of the clouds deduced from
the polarization data, after correction for foreground ISM contamination, are
seen to be connected to the ambient B-fields on the large scale. They seem to
play an important role in shaping the cloud IC1396A and BRC 37. BRCs 38 and 39
show a broader and snubber head morphology possibly due to the B-fields being
aligned with incoming radiation as explained in the simulations. A good general
agreement is noted on comparing our observational results with the simulations
supporting the importance of B-fields in BRC evolution. This work is the first
step towards systematic mapping the B-fields morphology in multiple BRCs in an
expanding H II region, extending the work presented by Soam et al. (2017b).
