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

Using the relation,
`(1)/(f)=(1)/(u)+(1)/(v)`, we get
`(1)/(v)=(1)/(f)-(1)/(u)=(1)/(15)-((1)/(-12))`
`therefore v=(20)/(3)cm=+6.67cmapprox6.7 cm`
The positive sign shows that the image is formed behined the mirror.
Using the relation,magnificient `m=-(u)/(v)`, we get
`m=-((20//3))/(-12)+(5)/(9)`
Hence, the image is virtual, erect and diminshed.
As the needle is moved farther from the mirror, the image move towards the focus (upto the focus only) and gets smaller and smaller in size.