A thin rod of length `d//3`is placed along the principal axis of a concave mirror of focal length `=d`such that its image,which is real and elongated,just touches the rod.Find the length of the image?

Answer

`d//2`

Explanation

image of`A` is itself at on`A`.Images of`B`is at`B'`
`(1)/(v)+(1)/(u)=(1)/(f)implies =1/(v_(B))-(3)/(-5d)=1/(-d)rArr(1)/(v_(B))=-(1)/(d)+(3)/(5d)`
`(1)/(V_(B)')=(-5+3)/(5d)rArrv_(B)^(')=(-5d)/(2)`
Length of image=`|v_(B)^(')-v_(A)'|rArr` Length of image =`(5d)/(2)-2d`
Length of image=`(d)/(2)`