The critical divergence of the smectic-order correlation lengths parallel and perpendicular to the director, xi( parallel, perpendicular), and the susceptibility, sigma(0), near the nematic-to-smectic-A phase transition has been measured in a 5 T magnetic field. The high magnetic field reduced the mosaicity and improved the effective transverse resolution by almost 2 orders of magnitude and permitted measurements nearly over four decades of reduced temperature. The results provide important new insights into mosaicity correction. The values of the critical exponents of xi( parallel, perpendicular) and sigma(0) were nu( parallel) = 0.79+/-0.02, nu( perpendicular) = 0.68+/-0.02, gamma = 1.45+/-0.04, respectively. They become smaller for a narrower nematic range.