A screen is placed 90 cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20 cm. Determine the focal length of the lens.
The image of the object can be located on the screen for two-position of convex lens such that u and v are exchanged. The separation between two positions of the lens is, d= 20 cm From the figure, u1+v1=90cm v1−u1=20cm Solving, v1=55cm, u1=35cm From lens formula, v1−u1=f1 551−−351=f1 ⇒f1=551+351=9055×35 ⇒f=21.4cm
