Three lenses `L_1,L_2,L_3` each of focal length `30 cm` are placed co-axially as shown in (Fig. 11(b).57).
An object is held at `60 cm` from the optic centre of lens `L_1`. The final real image is formed at the focus of `L_3`. Calculate separation between
(i) `L_1` and `L_3`
(ii) `L_2` and `L_3` ?
.

Explanation

For lens `l_1 , u = -60 cm, f = + 30 cm`.
If `v_1` is distance of image `I_1` from `C_1`, then from
`(1)/(v_1)-(1)/(u)=(1)/(f_1)`
`(1)/(v_1)=(1)/(f_1)+(1)/(u)=(1)/(30)-(1)/(60)=(1)/(60)`
`v_1 = 60 cm = C_1 I_1`
As final image `I` is at focus of `L_3`, therefore, rays falling on `L_3` must be parallel tom commen principal axis. For this to happen, `I_1` must be at the focus of `L_2`. Hence distance between `L_1 L_2` is
=`C_1 C_2 = C_1 I_1 + I_1 C_2 = 60 cm + 30 cm = 90 cm`
and distance between `L_2 and L_3` can have any reasonable value, as rays between `L_2` and `l_3` are parallel rays. The course of rays in shown in Fig.
.