Sharp image of extended object which is placed perpendicular to the principle axis of a lens is `eta` times that of the object for a particular position of object on a screen. Without disturbing the position of object and screen, by shifting lens a position can be obtained where the sharp image is `1//eta` times that of object. Ratio of difference between the two positions of lens to the focal length of lens is:

Options

A. `(eta^(2) -1)/(eta)` if `eta gt 1`
B. `(eta^(2)-1)/(eta)` if `eta le 1`
C. `(eta^(2) -1)/(eta)` for all values of `eta`
D. `eta`

Answer

C