Two convex lenses f focal length 20 cm each are placed coaxially with a separation of 60 cm between them. find the image of a distance object formed by the combination by a. using thin les formula separately for the two lenses and b. using the equivalent lens. Note that although the combination forms a real image of as distance object on the other side, it is equivalent to as diverging lens as far as the locatiion of the final image is concerned.

Explanation

a. The first image is formed at the focus of the first lens. Ths is at 20 cm from the first lens and hence at `u=-40` cm from the second. Using the lens formula for the second lens
`1/v=1/u+1/f=1/(40cm)+1/(20cm)`
or `v=40 cm`
The fiN/Al image is formed 40 cm to the right of the second lens.
b. The equivalent focal length is
`1/F=1/f_1+1/f_2-d/f_1f_2`
`=1/(20cm)+1/(20cm)-(60cm)/((20cm)^2)`
or `F=-20cm`
It is a divergent lens. It should be be kept at a distance `D=(dF)/f_1` behind the secod lens.
`Here D=((60cm)(-20cm))/(20cm)=-60cm`
gt Thus teh equivalent lens shoud be placed at a distance of 60 cm to the right of the second lens.The fiN/Al image is formed at the focus of this divergent lens i.e., 20 cm to the left of it. It is therefore 40 cm to the right to the second lens.