Magnetron discharges are widely used as sputtering sources for thin film deposition. Despite the importance of the sheath region where the electric field can be very high, there have been few experimental investigations of this region in magnetron plasmas. We report values of the sheath thickness deduced from measurements of the electric field distribution using laser spectroscopy. With this technique, a transition which is normally forbidden becomes in the presence of an electric field partially allowed so that laser induced fluorescence on this transition can be used as a measure of the electric field. It was found that the sheath thickness was approximately equal to the maximum displacement, in the absence of collisions, of a secondary electron from the cathode surface.