We use images collected with the near-infrared camera (NIRCam) on board the James Webb Space Telescope and with the Hubble Space Telescope (HST) to investigate multiple populations at the bottom of the main sequence (MS) of 47 Tucanae. The m F115W vs. m F115W −m F322W2 CMD from NIRCam shows that, below the knee, the MS stars span a wide color range, where the majority of M-dwarfs exhibit blue colors, and a tail of stars are distributed toward the red. A similar pattern is observed from the m F160W vs. m F110W − m F160W color-magnitude diagram (CMD) from HST, and multiple populations of M-dwarfs are also visible in the optical m F606W vs. m F606W − m F814W CMD. The NIRCam CMD shows a poorly-populated sequence of faint MS stars that we tentatively associate with a population of very low-mass stars. We introduce a chromosome map of M-dwarfs that reveals an extended first population and three main groups of second-population stars. By combining isochrones and synthetic spectra with appropriate chemical composition, we simulate colors and magnitudes of different stellar populations in the NIRCam filters (at metallicities [Fe/H]=-1.5 and [Fe/H]=-0.75) and identify the photometric bands that provide the most efficient diagrams to investigate the multiple populations in globular clusters. Models are compared with the observed CMDs of 47 Tucanae to constrain M-dwarfs' chemical composition. Our analysis suggests that the oxygen range needed to reproduce the colors of first-and second-population M-dwarfs is similar to that inferred from spectroscopy of red giants, challenging the proposal that the chemical variations are due to mass transfer phenomena in proto-clusters.