In an optical-bench experiment, the distance between an illuminated object pin and a fixed screen is 90 cm. A thin convex lens is placed between the object and the screen and a sharp image is obtained on the screen for two distinct positions of the lens. The two positions of the lens are 20 cm apart.
(i) Show that the focal length f of the lens can be expressed in terms of the object-screen separation D and the distance d between the two lens positions as f=4DD2−d2 .
(ii) Using the given numerical values, calculate the focal length of the lens.