This thesis focuses on two experiments done at the National Institute of Standards and Technology (NIST) to measure neutron scattering lengths. Both experiments used a neutron interferometer; a device that has been used to determine the scattering lengths of a variety of isotopes to better than one percent relative uncertainty. Neutron scattering lengths are important parameters in understanding both nucleon structure and nucleon-nucleon interactions from the point of view of low-energy quantum chromodynamics (QCD) The first experiment is an attempt to measure the neutron-electron scattering length bne. The neutron-electron scattering length is important because of its relationship to the internal charge distribution of the neutron. Combining the latest bne results gives the current excepted value of bne = (-1.345 +/- 0.025) 10-3 fm. However, there is a non-statistical disagreement between the individual measurements. Here we use a neutron interferometer to measure the large-dynamical phase shift, part of which is due to bne, caused when the neutron and crystal satisfy Bragg's law. This is accomplished by rotating a perfect silicon crystal in steps as small as 10-8 rad through the Bragg condition. Because of unforeseen signal losses, this experiment has not yet produced a final result but lessons learned in this work will assist future bne measurements The second experiment is a measurement of the spin-incoherent neutron scattering length of 3He b'i. In the study of few-body nuclear physics, two and three nucleon potentials are used to describe complex nucleon interactions which cannot be directly calculated using QCD. Neutron scattering lengths of light isotopes provide crucial tests of these nucleon-nucleon potentials. The neutron interferometry and optics facility at NIST had been used previously to determine the spin-coherent scattering lengths for n-1H, n-2H, and n-3He to better than 0.2% relative uncertainty. We report a result of b' i = (-2.512 +/- 0.018) fm using a polarized 3He target and polarized neutron beam. This result combined with spin-coherent data is in good agreement with certain theoretical models describing three nucleon interactions