Class 12 Physics practical reading To find the focal length of a convex lens by plotting a graph between u and v or between 1/u and 1/v.

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. 

Apparatus Required 

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

Theory 

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

Ray diagram

Procedure 

1. Get a sharp image of a distant object (say a tree) on a wall or a screen. Measure the distance between the lens and the wall. Record it as approximate focal length of a lens. 

2. Place the lens upright near the middle of the optical bench and the two needle uprights on either side of the lens. 

3. Adjust the levelling screws provided in the optical bench to make the lens vertical. Ensure that the principal axis of the lens is parallel to the optical bench scale. 

4. Note the position of the index mark at the base of lens upright. Keep the object pin at a position so that its tip and teh centre of the lens are separated a distance equal to the length of the given knitting needle (say x cm). Record the positions of the index mark of the object pin and the lens uprights on the bench. Calculate the difference in the positions of the lens and the object pin, say y cm The index correction for the object distance u is (x - y) cm. This correction is algebraically added to the object distance. 

5. Repeat step 4 to find the index correction for the image distance between the lens and the image pin. 

6. Keep the object pin at a distance of nearly 1.5 times the approximate focal length. Adjust the height of the needle, equal to the optical center of the lens. Keeping one eye closed and looking from the other side of the lens, locate the clear inverted image of the pin. It will appear to be enlarged. 

7. Keep the image pin at a distance of more than double the rough focal length. Adjust its heights so that the tip of the needle just coincides with the inverted tip of the image of the other needle. To differentiate between the two, insert a piece of paper on the tip of one of the needles. Use lateral (side ways) motion screw to make the tips coincide. 

8. Move the eye sideways and see that there is no parallax between the image needle and the image of the object needle. If need be, move the image needle forward or backward. When the parallax is removed, the tips will coincide and they will appear to be coinciding for all positions of the eye.

9. Record the positions of the index marks of the lens, the object pin and image pin from the scale of the optical bench. 

10. Change the position of the object pin by a small distance (say 2 cm) away from the lens and readjust the image pin to record at least five different sets of observations.

Observations 

Graph between -u & v

Graph between -1/u & 1/v

Precautions 

1. The tips of needles and the optical centre of the lens should be at the same height. 

2. The uprights should be vertical. 

3. Parallax should be removed from tip to tip. 

4. Proper index correction should be applied. 

5. The experiment should be performed in a well-lit room.

Sources of Errors

1. The needles are not at the same height. 

2. Index corrections not properly applied. 

3. Parallax not removed.