Find the Focal Length of a Convex Lens by Plotting u–v and 1/u–1/v Graphs

Aim

To find the focal length of a convex lens by plotting a graph between u and v or between 1/u and 1/v.

An optical bench, three uprights, a convex lens, a lens holder, two optical needles, a knitting needle, and a metre scale.

The focal length ( f ) of a convex lens is related to the object distance ( u ) and image distance ( v ) by the lens formula:

Obtain a sharp image of a distant object on a wall/screen and measure the distance between the lens and the wall. This gives an approximate focal length.
Mount the convex lens at the centre of the optical bench with two needle uprights on either side.
Adjust the levelling screws of the bench so that the optical axis is horizontal and the lens remains vertical.
Note the index mark at the base of the lens upright.
Place the object pin such that the separation between its tip and the lens centre equals the length of the knitting needle (x cm).
Record the positions of both uprights.
The index correction for object distance ( u ) = ( x - y ) cm, where ( y ) is the measured separation.
Apply this correction algebraically.
Repeat step (4) similarly for the image pin to find index correction for ( v ).
Keep the object pin at about 1.5 times the approximate focal length. Adjust its height to align with the optical centre of the lens. Observe the enlarged inverted image.
Keep the image pin at more than twice the rough focal length. Adjust height and lateral position so that the tip of the image pin coincides with the inverted image of the object pin.
Remove parallax by moving the eye sideways; adjust until the two tips remain coincident for all positions.
Record the index marks for lens, object pin, and image pin.
Shift object pin by ~2 cm repeatedly and record at least 5 sets of readings.