An object is placed 20cm to the left of a converging lens having focal length 16cm. A second, identical lens is placed to the right of the first lens, such that the image formed by the combination is of the same size and orientation as the object is. Find the separation between the lenses.

Answer

160

Explanation

For `L_(1)` , from lens formula,
`(1)/(v)-(1)/(-20)=(1)/(16),rArr(1)/(v)=(1)/(16)-(1)/(20)`
`rArr v=20cm`
`[` image is real, inverted, andn magnified `]`
`m_(1)=(v)/(u)=(80)/(-20)=-4`
Let `2^(nd)` lens is at a distance of x cm from `I_(1)` Since final image has to be erect w.r.t. original object, it has to be inverted and diminished w.r.t. `I_(1)` .
For `L_(2), u=-x, v=v, m_(2)=-(1)/(4)`
So, `(v)/(-x)=-(1)/(4)rArr v=(x)/(4)`
Now, from tlens formula,
`(1)/(v)-(1)/(u)=(1)/(f)`
`(1)/(x//4)-(1)/(-x)=(1)/(16) `
`(5)/(x)=(1)/(16)rArr x=80cm`
Hence, the separation between the lenses is 160cm.