A real image of an object is formed at a distance of `20 cm` from a lens. On putting another lens in contact with it, the image is shifted `10 cm` towards the combination, Determine the power of the second lens.

Explanation

Here, as image formed by the lens is real, the lens must be convex, `v = 20 cm`. If `f_1` is focal length of this lens, them from
`(1)/(v)-(1)/(u)=(1)/(f_1)`
`(1)/(20)-(1)/(u)=(1)/(f_1)` …(i)
For the combination (of focal length f),
`v = (20 - 10)cm = 10 cm`
:. `(1)/(10)-(1)/(u)=(1)/(f)=(1)/(f_1)+(1)/(f_2)`
using (i), `(1)/(10)-(1)/(u) = ((1)/(20) - (1)/(u)) + (1)/(f_2)`
or `(1)/(10)-(1)/(20) = (1)/(f_2)`
or `f_2 = 20 cm`
`P = (100)/(20) = 5 dioptre`.