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

Given u + v = 90
`(v)/(u) = 2 implies v = 2u`
From eq.(i) and (ii) , we get
u = 30 cm v = 60 cm
As f = `(uv)/(u - v)`
`therefore f = (-1800)/(-30 - (+60)) = (-1800)/(-90) = 20` cm
`therefore` Focal length and nature of lens req. is 20 cm and convex lens respectively .