A converging lens of 20 cm focal length and 5 cm diameter is cut along the line AB. The part of the lens shown shaded in the diagram is now used to form an image of a point object P placed 30 cm away from it on the line XY, which is perpendicular to the plane of the lens. The distance of image of P will be formed from XY line is $N/2 cm,$ then N is_____

When a part of a lens is used to form an image, it forms the same image as the whole lens. Also, the optic axis of this part is the same as the optic axis of the entire lens. Here, CD is the optic axis of the original lens and hence also of the part of the lens used here. P will then behave as an object placed 0.5 cm away from CD, i.e., as an object OP of height $0.5 cm.$
Using  $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ we get v= 60 cm.
Magnification,  $M=\left|\frac{v}{u}\right|=2$ for the image IQ.
Thus  $\frac{IQ}{OP}=2orIQ=1cm$
Q is the image of P, formed 1 cm below CD or 1.5 cm below XY.