The ellipsometric measurement of the thickness of thin oxide films on copper and, in particular, the computational technique for the solution of the reflection equations for an unknown, absorbing film is discussed. The experimental results were not of sufficient accuracy to allow a unique solution of the equations to be obtained, but they did indicate ranges within which the solutions should lie. Theoretical solutions using these ranges were calculated and were found to be in good agreement with the experimental results. The effect of thin absorbing surface films on the calculated optical constants of substrates is also discussed.