Redshift estimate of a gravitational lens from the observed reddening of a multiply imaged quasar

Light rays from a multiply imaged quasar usually sample different path lengths across the deflector. Extinction in the lensing galaxy may thus lead to a differential obscuration and reddening between the observed macro-lensed QSO images. These effects naturally depend on the precise shape of the extinction law and on the redshift of the lens. By means of numerical Monte-Carlo simulations, using a least-squares fitting method and assuming an extinction law similar to that observed in the Galaxy, we show how accurate photometric observations of multiply imaged quasars obtained in several spectral bands could lead to the estimate of the lens redshift, irrespective of the visibility of the deflector. Observational requirements necessary to apply this method to real cases are thoroughly discussed. If extinction laws turn out to be too different from galaxy to galaxy, we find out that more promising observations should consist in getting high signal-to-noise low resolution spectra of at least three distinct images of a lensed quasar, over a spectral range as wide as possible, from which it should be straightforward to extract the precise shape of the redshifted extinction law. Very high signal-to-noise, low spectral resolution, VLT observations of H 1413+117 and MG 0414+0534 should enable one to derive such a redshifted extinction law.