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.
a. (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 .
b. (ii) Using the given numerical values, calculate the focal length of the lens.