Two convex lenses, each of focal length 15 cm, are placed at a separation of 20 cm with their principal coinciding.
(i) Show that a light beam coming parallel to the principal axis diverges as it comes out of the lens system.
(ii) Find the location of the virtual image formed by the lens system of an object placed far away.
(iii) Find the focal length of equivalent lens.

Explanation

(i) Consider combination of lenses

(ii) Image by `L_(1)`, at a distance 15 cm right of it
Image by `L_(2)`,`I_(1)` acts object for it
`1/v-1/(-5)=1/15`
`rArr1/v=-2/15rArrv=-7.5 cm`
7.5 cm left of `L_(2)`
(iii) Focal length of two equivalent lens,
`1/F=1/(f_(1))=1/(f_(2))-d/(f_(1)f_(2))=1/15+1/15-20/100=-1/15`
F=-15cm
Note That the sign of the focal length is negative and the lens system is diverges a parallel beam incident on it.