Question

An object is placed at a distant of `1.50` from a screen and a convex lens placed in between produces an image magnified `4`times on the screen .What is the focal length and the position of the lens.

Answer 1

The information given in the question ray diagram.It is given that
`m=(1)/(O)=-4`
Lets lens is placed at a distance of`x` from the object.Then
u=-x,and v=(1.5-x)
using`m=(v)/(u),"we get"-4=(1.5-x)/(-x)`
or 4x=1.5-x
or 5x=1.5
Thus x=0.3 metre
The lens is placed at a distance of 0.3m from the object (or`1.20m`from the screen)
For focal length,we may use
`m=(f)/(f+u)`
or`-4=(f)/(f+(-0.3))`
or`-4f+1.2=f`
or`5f=1.2`
thus`f=(1.5)/(5)=0.24`
The focal length is `0.24m(or 24cm)`