A magnifying lens has a focal length of 10 cm. (a) Where should the object be placed if the image is to be 30 cm from the lens ? (b) What will be the magnification ?

Explanation

`f=+10cm`
`v=+-30 cm`
Case 1. `v=+30 cm`
`(1)/(v)-(1)/(u)=(1)/(f)implies(1)/(30)-(1)/(u)=(1)/(10)impliesmu=-15cm`
`m=(v)/(u)=(+30)/(-15)=-2`
If the object is placed `15 cm` before the lens, a real image is formed `30` cm away from the lens. Its magnification is `2` and the image is inverted.
Case 2. `v=-30cm`
`(1)/(v)-(1)/(u)=(1)/(f)`
`(1)/(-30)-(1)/(u)=(1)/(10)impliesu=-7.5cm`
`m=(v)/(u)=((-30)/(-7.5))=+4` .
If the object is placed, `7.5` cm before the lens, a virtual image is formed `30` cm from the lens. It is `4` times enlarged and erect.