Two lenses of power `+ 10 D and - 5 D` are placed in contact,
(i) Calculate the focal length of the combination
(ii) where should an object be held from the combination so as to obtain a virtual image of magnification `2` ?

Answer

(i) `20 cm`
(ii) `- 10 cm`

Explanation

(i) Here, `P_(1) + 10 D, P_(2) = - 5D`
`P = P_(1) + P_(2) = + 10 - 5 = 5D`
`F = (100)/(P) cm = (100)/(5) = 20 cm`
(ii) `m = + 2`, as image is virtual
From `m = (f)/(u + f)`
`2 = (20)/(u + 20)`
`2u + 40 = 20`
`u = (20 - 40)/(2) = - 10 cm`