Attenuation caused by a distant Isothermal Turbulent Screen

We analyse in detail the attenuation caused by an isothermal turbulent distant foreground dust screen. The attenuation curve is well determined by two parameters, the absolute-to-relative attenuation ratio R^A_V=A_V/E(B-V) and the absolute attenuation A_V. We show quantitatively how these two observable quantities depend on the statistical properties of the local density and the mean attenuation <A_V> and how they vary with the thickness of the screen measured in units of the largest turbulent scale. The attenuation through a turbulent medium is characterised by higher transparency and a flatter attenuation curve in comparison with a homogeneous dust screen. In general, the effect of the turbulent medium on the attenuation increases with slice thickness. In the limit of thick slices, typically larger than the maximum turbulent scale, R^A_V asymptotically approaches a maximum value.