### DISPLACEMENT METHOD TO DETERMINE THE FOCAL LENGTH OF A CONVEX LENS

**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**

On solving

__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.

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