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.

Explanation

Let u be the object distance and v be the image distance. For a lens the positions of the object and the image are interchangeable. In the following figure the two positions mentioned in the question have been shown as `P_(1) and P_(2)`.

Distance between object and image
`D=90cm=u+v`
Distance between two position of lens
`d=20cm = v-u`
`therefore" "u=35cm and v=55cm`
From lens formula,
`(1)/(f)=(1)/(55)+(1)/(35)=(18)/(385)`
`f=(385)/(18)=21.38cm`