If the distance D of an object between an object and screen is greater than 4 times the focal length of a convex lens, then there are two positions of the lens between the object and the screen at which a sharp image of the object is formed on the screen. This method is called displacement method.
Let U = distance of an object from a convex lens.
F = focal length.
V = D – U = the distance of image from the lens.
From lens formula
Now, there are following possibilities:
(a) If D < 4 f, then u is imaginary.
So, physically no position of the lens is possible.
(b) If D = 4 f, then. So only one position is possible. The minimum distance between an object and its real image in case of a convex lens is 4 f.
(c) If D > 4 f, there are two positions of the lenses at distances and
Since v = D –u. Therefore
Let the lens be displaced through x,
Let and be the magnification for the first position of lens and second position of the lens.