A thin rod of length`(f)/(3)`is placed along the optic axis of a concave mirror of focal length f such that its image which is real and elongated, just touches the rod. The magnification is …..

Explanation

`:'` image C and E . One end A of the image coinicids with the end A of rod itself
`So V_(A) = u_(A ) , (1)/(V_(A)) + (1)/(V_(A)) = (1)/(- F)`

i.e., `V_(A) = u_(A) =- 2f`
so if clear that the end A is at C
`:' ` the length fo rod is `(f )/( 3)`
`:. ` distance of the other end B from P is
`u_(beta)= 2 f - ( f)/( 3) = (5 )/(3 ) f`
if the distance of image of end B from P is `V_( beta)` then
`(1)/( V_(B)) + (1)/((5)/(3 )f) = (1)/( - f) ` i.e, `V_(B) = (5)/(2 ) f`
`:. ` the size of the image
`|V_(B) | - |V_(A)| = (5)/(2) f - 2f = (1)/(2 ) f`
and magnification `m= (V_(B) -V_(A))/( u_(beta ) - u_(A))= ((1)/(2) f)/(-(1)/(2)f ) =- (3) /(2)`
Negative sing implies that image is inverted with respect to object and so it is real .