A thin convex lens of focal length 25 cm is cut into two pieces 0.5 cm above the principal axis. The top part is placed at (0,0) and an object placed at (–50 cm, 0). Find the coordinates of the image.
Let AB be the principal axis of the convex len. Focal length, f=25cm since it cut into the piece 0.5cm above the principal axis. The top part placed at (0,0) and object is at (50,0) So, Object distance, u=50cm Let, the image distance be v. Now, by using lens formula: ∴v1−u1=v1=f1+u1 v1=251−501=501 v=50cm And, we know, The magnification can be given as m=uv=−5050=−1 Hence image is inverted. so, h′=m×h=−1×0.5=−0.5cm This would have formed 50cm from the pole and 0.5cm below the principal axis. Hence, with respect to x-axis passing through the edge of the cut lens, the co-ordinates of the image are, (50cm,(−0.5−0.5)cm)=(50cm,−1cm) ∴ co-ordinates of the imag are (50cm,−1cm)
