An illuminated object and a screen are placed `90 cm` apart. What is the focal length and nature of the lens required to produce a clear image on the screen twice the size of the object ?

Explanation

As image is real, the lens must be convex and it should be placed between the object abd screen. Let `x` be distance between the object and convex lens.
`:. u = -x, v = 90 - x , m = -2`
As `m = (v)/(u)`,
`:. -2 = (90 - x)/(- x). X = 30 cm`
`:. u = -x = -30 cm`,
`v = 90 - x = 90 - 30 = 60 cm`
`(1)/(f)=(1)/(v)-(1)/(u)=(1)/(60)-(1)/(-30)=(1)/(20)`
`f = 20 cm`.