We estimate the optical depth distribution of dust present in absorption systems along the line of sight of high redshift galaxies and the resulting reddening .
We characterize the probability distribution of the transmission to a given redshift and the shape of the effective mean extinction law by means of analytical estimates and Monte Carlo simulations .
We present our results in a format useful for applications to present samples of high redshift galaxies and discuss the implications for observations with the James Webb Space Telescope .
Our most realistic model takes into account the metallicity evolution of Damped Lyman \alpha absorbers and predicts that the effects of dust absorption are modest : at redshift z \gtrsim 5 the transmission is above 0.8 at an emitted wavelength \lambda _ { e } = 0.14 \mu m with probability 90 \% .
Therefore dust obscuration along the line of sight will affect only marginally observations at very high redshift .