The critical divergence of the smectic-order correlation lengths parallel and perpendicular to the director, ξ∥,⊥, and the susceptibility, σ0, 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 ξ∥,⊥ and σ0 were ν∥ = 0.79±0.02, ν⊥ = 0.68±0.02, γ = 1.45±0.04, respectively. They become smaller for a narrower nematic range.