The neutron coherent scattering length bc has been determined interferometrically to an uncertainty of about 5x10-5 by measuring the nondispersive phase.We propose improving the uncertainty to about 10-6 by optimizing various para-meters of the interferometric experiment.Any uncertainty inthe bc determination arising from possible variations in the constitution of the ambient air can be eliminated by performing the experiment in vacuum.When such uncertainty is attained,it becomes necessary to account for the neutron beam refraction at the sample-ambient interfaces,to infer the correct bc from the observed phase.The formula for the phase used hitherto is approximate and would significantly over estimate bc.There fractive index for neutrons cant hus be determined to a phenomenal uncertainty of about 10-12