Two convex lenses each of focal length 10 cm, are placed at a saparation of 15 cm with their principal axes coinciding. (a) Show that a light beam coming parallel to the principal axis diverges as it comes out of the lens system. (b) Find the location of the virtual image formed by the lens system of an object placed far away. (c ) Find the focal lenth of the equivalent lens.

Explanation

(a),(b)
Image by `L_1`: at distance 10 cm right of it
Image by `L_2`: `I_1` acts object for it
`(1)/(v)-(1)/(-5)=(1)/(10)implies(1)/(v)=-(1)/(10)`
`v=-10cm`
`10cm` left of `L_2`
(c) `(1)/(F)=(1)/(f_1)+(1)/(f_2)-(d)/(f_1f_2)=(1)/(10)+(1)/(10)-(15)/(100)=(5)/(100)`
`F=20cm`