An infinitely long rod lies along the axis of a concave mirror of focal length f. The near end of the rod is distance `u gt f` from the mirror. Its image will have length

Options

A. `(f^(2))/(u-f)`
B. `(uf)/(u-f)`
C. `(f^(2))/(u+f)`
D. `(uf)/(u+f)`

Answer

A

Explanation

The image of end B will be at focus F.
For iamge of A,
`(1)/(v_(A))+(1)/(-u)=(1)/(-f) or v_(A)=((uf)/(u-f))`
Thus length of the iamge

`=v_(A)-f=((uf)/(u-f))-f=((f^(2))/(u-f))`.