The arc tube is provided with a mercury-free arc tube main body that has a discharge light-emitting portion (closed glass sphere), and a cylindrical shroud glass tube that is airtightly integrated with the arc tube main body. In the mercury-free arc tube in which an inert gas is sealed in the shroud glass tube that surrounds the closed glass sphere, in the shroud glass tube, the adjustment is made so as to satisfy the light flux and the life span with respect to the pressure X (atmospheric pressure) of a rare gas sealed in the closed glass sphere, and an amount M (mg/ml) of sealed metal halide.