The visible and dark sectors of particle physics can be connected via the kinetic mixing between the ordinary (γ) and hidden photon (γ′). If the latter is light its production in high energy collisions of ordinary particles occurs via the γ − γ′ oscillations similarly to the neutrino processes. Generically, the experiments are insensitive to mass of the hidden photon, if it is lighter than 1 MeV, and it does not decay into e+e−-pair. Still, one can use the missing energy and scattering off the detector as signatures to search for light hidden photon. Presence of media suppresses production of the light vectors making the experiments insensitive to the entire model. In media the light hidden photon production is typically suppressed due to the dump of the γ − γ′ oscillations making the experiments insensitive to the entire model. We present analytic formulas for the light hidden photon production, propagation and detection valid for searches at colliders and beam-target experiments and apply them to estimate the impact on the sensitivities of NA64, FASER, MATHUSLA, SHiP, T2K, DUNE and NA62 for the background-free case.