Abstract: A high pressure sodium lamp includes an arc tube having an inner diameter greater than 12 mm. An amalgam including a prescribed quantity of sodium and mercury is sealed in the arc tube. To achieve the maximum lamp efficiency in different values of the inner diameter of the arc tube, the lamp should satisfy the following relationships:(10.sup.0.848 .phi..sup.(-0.171) log X+(0.105.phi.-10.22)<log Y<(10.sup.0.848 .phi..sup.(-0.171) log X-10.sup.1.43 .phi..sup.(-0.574)), and(-7.97 log.phi.+14.8)<log .DELTA.V<(84.7 log.phi.-84.5)where .phi. (mm) is the inner diameter of the arc tube, X (wt %) is the ratio of the quantity of sodium to the quantity of amalgam sealed in the arc tube, Y (mg/cc) is the quantity of sodium sealed in the arc tube, and .DELTA.V (v/cm) is the electric field strength when the lamp is operated.