For irradiating a layer a radiation beam is directed and focussed to a spot on the layer, relative movement of the layer relative to the lens is caused so that, successively, different portions of the layer are irradiated and an interspace between a surface of the lens nearest to the layer is maintained. Furthermore, at least a portion of the interspace through which the radiation irradiates the spot on the layer is maintained filled with a liquid, the liquid being supplied via a supply conduit. At least a portion of the liquid fills up a recess through which the radiation irradiates the spot.