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 ?

Answer

20 cm, convex lens.

Explanation

Here, `-u + v = 90 cm, f = ?`
As image on the screen is real, therefore,
`m = -2 = (v)/(u) , v = -2 u`
:. `-u - 2 u = 90 cm , u = - 30 cm, v = 60 cm`
`(1)/(f)=(1)/(v)-(1)/(u)=(1)/(60)+(1)/(30) = (1 + 2)/(60) = (3)/(60) = (1)/(20)`
`f = 20 cm`. This lens is convex.