Question

An object is placed at a distance of 75 cm from a screen. Where should a convex lens of focal length 12 cm be placed so as to obtain a real image of the object?

Answer 1

`D=75cm,f=12cm`
`Dgt4f`, there will be two positions of lens for which real image can be obtained
for lens in position (1): `u=-x,v=D-x=75-x,f=12cm`
`(1)/(v)-(1)/(u)=(1)/(f)implies(1)/(75-x)-(1)/(-x)=(1)/(12)`
`(75)/((75-x)x)=(1)/(12)impliesx^2-75x+900=0`
`(x-15)(x-60)=0`
`x=15` or `60cm`