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. Describe what happens as the needle is moved farther from the mirror.

Explanation

Given, object.s height, `h_(0)=4.5cm`
Focal length, `f=15cm" (convex mirror)"`
Using mirror formula,
`(1)/(u)+(1)/(v)=(1)/(f)`
`rArr" "-(1)/(12)+(1)/(v)=(1)/(15)`
`rArr" "(1)/(v)=(1)/(12)+(1)/(15)=(5+4)/(60)`
`=(9)/(60)=(3)/(20)`
`rArr" "v=(20)/(3)=6.7cm`
Image is virtual and erect and is formed behind the mirror.
`"Also, "(h_(i))/(h_(o))=-(v)/(u)`
`rArr" "(h_(i))/(4.5)=-(20)/(3xx(-12))`
`therefore" "h_(i)=(20xx4.5)/(3xx12)=2.5cm" (diminished)"`
As the needle is moved farther from the mirror, the image moves towards the focus (but never beyound) and gets progressively diminished in size.