In a screw-nut assembly (shown below) the nut is held fixed in its position and the screw is allowed to rotate inside it. A convex lens (L) of focal length 6.0 cm is fixed on the nut. An object pin (P) is attached to the screw head. The image of the object is observed on a screen Y. When the screw head is rotated through one rotation, the linear distance moved by the screw tip is 1.0 mm. The observations are made only when the image is obtained in the same orientation on the screen. At a certain position of P, the image formed is three times magnified as that of the pin height. Through how many turns should the screw head be rotated so that the image is two times magnified?