  Recent observation of linear optical polarization from brown dwarfs confirms
the dust hypothesis in the atmospheres of brown dwarfs with effective
temperature higher than 1400 K. The observed polarization could arise due to
dust scattering in the rotation induced oblate photosphere or due to the
scattering by non-spherical grains in the spherical atmosphere or by the
anisotropic distribution of dust clouds. Assuming single scattering by
spherical grains in a slightly oblate photosphere consistent with the projected
rotational velocity, the observed optical linear polarization is modeled by
taking grains of different sizes located at different pressure height and of
different number density. Minimum possible oblateness of the object due to
rotation is considered in order to constrain the grain size. It is shown that
the observed polarization from the L-dwarfs 2MASSW J0036+1821 and DENIS-P
J0255-4700 can well be explained by several sets of dust parameters and with
the minimum possible oblateness. Models for the observed polarization constrain
the maximum size of grains. It is emphasized that future observation of
polarization at the blue region will further constrain the grain size.
