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Gravitational lensing studies of the Bullet Cluster suggested convincingly infavor of the existence of dark matter. However, it was performed without theknowledge of the original orientation of each galaxy before gravitationallensing. A potential improvement to this issue lies in the measurement of theoriginal orientation from the polarization direction of radio waves emittedfrom each galaxy. In this context, Francfort et al. derived a formula that canutilize the information about the original orientation of each galaxy to obtainwhat is called {\it shear}. However, we demonstrate that shear in their formulashould be replaced by {\it reduced shear} when the change in sizes of images ofgalaxies is taken into account. As the previous gravitational lensing analysisof the Bullet Cluster used reduced shear, we suggest applying our improvedformula directly for the reanalysis once we obtain the polarization directionof radio waves. In particular, we show that our new formula can yield a moreaccurate analysis than the previous one, if the polarization direction can bemeasured more precisely than $10^\circ$. Moreover, the approach discussed inthis work is generically applicable to the gravitational lensing analysis ofclusters, not only limited to the Bullet Cluster.

New method to revisit the gravitational lensing analysis of the Bullet Cluster using radio waves