A diverging lens of focal length 20 cm and a converging lens of focal length 30 cm are placed 15 cm apart with their principal axes coinciding. Where should an object be placed on the principal axis so that its image formed at infinity ?

Explanation

(i) If final image is at infinite, for this image by one lens should be formed on focus of other.
Image by `L_1`:
`(1)/(v)-(1)/(-x)=(1)/(-20)implies(1)/(v)=-(1)/(20)-(1)/(x)=(-(20+x))/(20x)`
`v=-(20x)/((20+x))`
`(20x)/(20+x)+15=30implies(20x)/(20+x)=15`
`4x=60+3x`
`x=60cm`
(ii) Image by `L_1`:
`(1)/(35)-(1)/(-x)=(1)/(30)implies(1)/(x)=(1)/(30)-(1)/(35)=(7-6)/(210)`
`x=210cm`