We have investigated the absorption spectra in ultra small diameter single walled boron nanotubes for parallel and perpendicular polarized light as well as unpolarized light. In this paper we have studied absorption spectra for armchair (3,3),zigzag (5,0) and chiral (4,2) boron nanotubes containing 12, 20 and 56 atoms respectively. It is observed that absorption is highest for armchair followed by zigzag and chiral nanotubes. It is also found that absorption is higher for (3,3) and (5,0) nanotubes for perpendicular polarized light as compared to parallel polarized light, whereas chiral nanotube shows higher and wide range of absorption for parallel polarized light instead of perpendicular polarized light. We have compared our results with SWCNT and SWBNNT of same chiral vectors.