Expressions for the photovoltage and photocurrent of a strongly illuminated p-n junction solar cell are derived by solving the ambipolar diffusion equation. A complete boundary condition is derived for the junction, which is valid for all levels of injection. In the open-circuit case, results are in agreement with those given by earlier theories, while in the short-circuit case, the current is found to saturate at the ratio of the diffusion potential to the internal resistance. Results are used to explain the experimental results of earlier workers.