We report the first results on linear birefringence studies of dimeric crystals. The compounds investigated were CuX2.2TMSO, X = Br, Cl, two Heisenberg S = 1/2 antiferromagnetic dimers. The exchange constants derived from the birefringenc data are J (Br)/k = -23.0 K and J (Cl)/k = -13.0 K, in good agreement with previous estimates. This study demonstrates the feasibility of using birefringence to study interactions in cluster compounds