It is demonstrated that the use of a micrometric thin 39 K vapor cell (MTC) and saturated absorption (SA) spectroscopy allows the formation of narrow atomic lines in the transmission spectrum without unwanted cross-over resonances. Another important feature is the small characteristic magnetic field value B 0 = A h f / μ B of 39 K, significantly smaller than for Rb and Cs. As a consequence, decoupling of J and I can be observed at relatively low magnetic fields ∼300 G, which results in the formation of two groups of four spectrally-resolved and equidistantly-positioned atomic transitions having the same amplitude (each group corresponds to a given circular polarization σ ± ) which we record using a simple experimental setup with a linearly polarized tunable diode-laser and a longitudinal magnetic field obtained with two permanent magnets. Fabrication of a MTC is much easier than the fabrication of the 39 K nanocells used in our previous works. A simple method to determine the magnitude of a wide range of B -fields with a spatial resolution of 30 µ m is presented, which is intrinsically calibrated and does not require a frequency reference.