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_(1))/(h_(2)) = (-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.