A `5 cm` long needle is placed `10 cm` from a convex mirror of focul length `40 cm`. Find the position, nature and size of image of the needle. What happens to the size of image when needle is moved farhter away from the mirror ?

Explanation

Here, `h_1 = 5 cm, u = -10 cm`,
`f = 40 cm`
From `(1)/(v)=(1)/(f)-(1)/(u)=(1)/(40)-(1)/(-10)=(5)/(40)=(1)/(8)`
`v = 8 cm`
Image is virtual, erect and is formed `8 cm` behind the mirror.
Magnification, `m = (h_2)/(h_1) = (-v)/(u) = (-8)/(-10) = (4)/(5)`
`h_2 = (4)/(5) h_1 = (4)/(5) xx 5 = 4 cm`
As needle is moved farther away from the mirror, image shifts towards the focus and its size goes on decreasing.