Radial distribution of temperature in a thin lens due to absorption of light and heat conduction

We consider the stationary radial distribution of temperature in a lens. For a thin lens, i.e. a two-dimensional model problem, we give an analytical approximation for the distribution of temperature, a quantity of great importance for the prediction of the performance of the lens. We compare this formula with the numerical solution of the heat equation for several examples. Finally, we discuss the incorporation of the heat-transfer to the environment in principle and give prospects for further generalizations of this theory.