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A 5 cm long needle is placed 10 cm from ...

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 ?

Text Solution

Verified by Experts

Given, height of object, `h_(1)=+5cm`
Object distance, `u=-10cm`
Focal length, `f=+40cm` (convex mirror)
Using mirror formula,
`(1)/(v)=(1)/(f)-(1)/(u)=(1)/(40)-((-1)/(10))=(5)/(40)=(1)/(8)`
`rArr" "v=+8cm`
As v is positive the image is virtual and erect and is formed 8 cm behind the mirror.
`"Magnification, m"=(-v)/(u)=(h_(2))/(h_(1))`
`rArr" "(h_(2))/(5)=(-8)/(-10)`
`rArr" "h_(2)=(8)/(10)xx5=4cm`
As we move the needle away from the mirror, the image shifts towards the focus and its size keeps on decreasing. When the needle is very far off, it appears almost as a point image at the focus.
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