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