An arrangement of a concave and a convex lens is shown below. The focal length of the convex lens is 30 cm. Parallel rays coming from a distant source are focused on the screen after passing through the lenses. Calculate the focal length of the concave lens.

Explanation

In the absence of concave lens, parallel rays after passing through convex lens will converge at a distance 30 cm from it.
`therefore" Focal length of convex lens, "f_(1)=+30cm`
This point will act as a virtual object for the concave lens.
`"Object distance, "v=30-10=+20cm`
`"Image distance, "v=20+10=+30cm`
Let `f_(2)` be the focal length of the concave lens. Then,
`(1)/(f_(2))=(1)/(v)-(1)/(u)=(1)/(30)-(1)/(20)=-(1)/(60)`
`rArr" "f_(2)=-60cm`