We propose an order of magnitude improvement in the present five parts in 10⁵ precision of a nondispersive interferometric measurement of the neutron coherent scattering length b_c. For this purpose we make a judicious selection of the Bragg angle for the interferometer and the sample thickness. The precision is further improved by an optimal choice of the Bragg reflection (and a consequent neutron wavelength). By performing the experiment in vacuum, errors arising from possible variations in the pressure, composition or humidity of the ambient air can be eliminated. On attaining such precision, we ought 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 overestimate b_c. The refractive index for neutrons can thus be determined to a phenomenal precision of a few parts in 10¹².