^Displacement method

This method is used in the labs to find the focal length of a convex lens.

Consider an object placed between a thin convex lens of focal length ‘f’ & a screen at a distance ‘D’ from the screen.

Using Lens formula for this problem one can write:

To get two distinct images the discriminate > 0.

Thus the essential condition to get two distinct real images on the screen is D > 4 f.

From eqn. (1) the two roots of the quadratic i.e. two different distance of the lens from the object are given by:

From these relations the distance between the two positions of the lens (say ‘x’) can be written as:

The image distance can be written as:

This implies that for the two positions of the lens the image & object distances are interchangeable.

The magnification of the two images can be given by: