(a) 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 ?
(b). A pin length 2.00 cm is placed perpendicular to the principal axis of a converging lens. An inverted image of size 1.00 cm is formed at a distance of 40.0 cm fromthe pin. Find focal length of the lens and its distance from the pin.

Explanation

(a). `f=10cm,v=30cm,u=-x`
`(1)/(v)-(1)/(u)=(1)/(f)`
`(1)/(30)-(1)/(-x)=(1)/(10)implies(1)/(x)=(1)/(10)-(1)/(30)=(2)/(30)impliesx=15cm`
`m=(v)/(u)=(30)/(-15)=-2`
(b). `O=2cm,I=-1cm`
Inverted image can be formed by convex lens for real object.
`u=-x,v=40-x`
`(I)/(O)=(v)/(u)implies(-1)/(2)=(40-x)/(-x)rArrx=80-2xrArrx=(80)/(3)`
`u=-x=-(80)cm,v=40-x=40-(80)/(3)=(40)/(3)cm`
`(1)/(f)=(1)/(v)-(1)/(u)=(1)/((40)/(3))-(1)/((-80)/(3))-=(3)/(40)+(3)/(80)=(6+3)/(80)`
`f=(80)/(9)cm`