Attenuation caused by a distant isothermal turbulent screen

We analyze 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_V ^A = A_V/E(B - V) and the absolute attenuation Ay. 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 characterized by higher transparency and a flatter attenuation curve in comparison with a homogeneous dust screen. In general, the effect of a turbulent medium on the attenuation increases with slice thickness. In the limit of thick slices, typically larger than the maximum turbulent scale, R_V^A asymptotically approaches a maximum value.