We report a direct comparison of the amplitudes of Stokes spectra of the Fe i 630 nm and 1.56 μm lines produced by realistic MHD simulations with simultaneous observations in the same spectral regions. The Stokes spectra were synthesized in snapshots with a mixed polarity magnetic field having a spatially averaged strength, < B >, between 10 and 30 G. The distribution of Stokes V amplitudes depends sensitively on < B >. A quiet inter-network region was observed at the German VTT simultaneously with TIP (1.56 μm) and POLIS (630 nm). We find that the Stokes V amplitudes of both infrared and visible observations are best reproduced by the simulation snapshot with < B > = 20 G. In observations with 1 resolution, up to 2/3 of the magnetic flux can remain undetected.