A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification.

Explanation

`O = 4.5 cm, u = -12cm, f = 15 cm`
`(1)/(u)+(1)/(upsilon)=(1)/(f) rArr (-1)/(12)+(1)/(upsilon)=(1)/(15)`
`(1)/(v)=(1)/(12)+(1)/(15)=(5+4)/(60)=(9)/(60)=(3)/(20)`
`upsilon=(20)/(3)=6.7cm`
Image is virtual and erect and is formed behind the mirror.
`(I)/(O)=(-v)/(u) rArr (1)/(4.5)=(-20)/(3xx(-12))`
`I=(20xx4xx2)/(3xx12xx10)=2.5cm`
As the needle is moved further from the mirror, the image moves towards the focus and gets progressively diminished in size.