The time history of the optical reflectivity of a dense plasma at the confined interface of a planar aluminium - plastic target was recorded through the transparent material, during the shock emergence from the aluminium. The shock wave was produced by the irradiation of the aluminium side of the target with a long-pulse laser light at irradiances up to and the interface probed by a low-energy laser pulse. The reflectivity of the probe laser beam at the interface was recorded across the shocked region. In the central shocked region the reflected probe light decreases in less than 200 ps, as the shock arrives at the rear side, and remains nearly constant at later time. The experimental results are interpreted by employing a simple model. It is shown that the reflection at early times can be explained by Fresnel reflectivity of the aluminium which decreases due to a temperature rise and an absorbing plasma in front of the shock. At later time a WKB approximation is used to calculate the reflectivity from the critical density of the dense plasma at the shock front. This reflectivity is very sensitive to the electron - ion collision frequency which is measured by fitting the model and experimental results.