A Zehnder-Mach interferometer was used to study the free convection thermal boundary layer about a uniformly heated vertical plate and to derive the heat transfer coefficients connected with this situation. The experiments were performed when the plate was immersed in water and the steady state boundary layer, as well as its transient development from an initial state at rest and with uniform temperature to steady state condition, was investigated when a step function in the power input to the plate was applied. Results for the steady state runs agree very well with the results of an analysis by Sparrow and Gregg. The transient runs indicate that the temperature field in the fluid develops initially in the same way as for heat conduction into a semi-infinite solid. After a short transition period, the steady state condition is reached. The boundary layer grows with time in such a way that it increases at first with increasing time, reaches a maximum, and decreases again until it settles to its steady state value. The wall temperature and the local heat transfer coefficient can be predicted for the whole period from start to steady state by the solution for one-dimensional unsteady conduction or for the steady state boundary layer.