A convex lens of focal length `10 cm` is placed co-axially `5 cm` away from a concave lens of focal length `10 cm`. If an object is placed `30 cm` in front of the convex lens, find the position of final image formed by the combined system.

Explanation

For the convex lens,
`f = 10 cm, u = -30 cm`
`(1)/(v)=(1)/(f)+(1)/(u)=(1)/(10)-(1)/(30)=(1)/(15), v = 15 cm`.
As concave lens is at `5 cm` from convex lens, therefore image formed by convex lens is at `(15 - 5)cm = 10 cm` beyond concave lens.
For concave lens
`u = + 10 cm, f = -10 cm`
`(1)/(v)=(1)/(f)+(1)/(u)=-(1)/(10)+(1)/(10)=0` `:. v = oo`
i.e., final image is formed at infinity.