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Scattering and absorption of light by a homogeneous distribution ofintergalactic large dust grains has been proposed as an alternative,non-cosmological explanation for the faintness of Type Ia supernovae at $z\s im0.5$. We investigate the differential extinction for high-redshift sourcescaused by extragalactic dust along the line of sight.  Future observations of Type Ia supernovae up to $z\sim 2$, e.g. by theproposed SNAP satellite, will allow the measurement of the properties of dustover cosmological distances. We show that 1% {\em relative} spectrophotometricaccuracy (or broadband photometry) in the wavelength interval 0.7--1.5 $\mu$mis required to measure the extinction caused by ``grey'' dust down to $\deltam=0.02$ magnitudes.  We also argue that the presence of grey dust is not necessarily inconsistentwith the recent measurement of the brightness of a supernova at $z=1.7$ (SN1997ff), in the absence of accurate spectrophotometric information of thesupernova.Comment: Accepted by A&

Measuring the properties of extragalactic dust and implications for the Hubble diagram