We solve the general problem of mixing of electromagnetic and scalar or pseudoscalar fields coupled by axion-type interactions $L_{\text{int}} = g_{\phi}\phi \epsilon_{\mu \nu \alpha \beta} F^{\mu \nu} F^{\alpha \beta}$. The problem depends on several dimensionful scales, including the magnitude and direction of background magnetic field, the pseudoscalar mass, plasma frequency, propagation frequency, wave number, and finally the pseudoscalar coupling. We apply the results to the first consistent calculations of the mixing of light propagating in a background magnetic field of varying directions, which show a great variety of fascinating resonant and polarization effects.