Experiment: To find the focal length (f) of a convex lens by plotting graph between 1/u and 1/v.
The relation between the object distance u and the image distance v for a convex lens placed in air is
1/f = 1/v + 1/u
1/v = -1/u + 1/f
Comparing above equation with the standard equation of a straight line, y = mx + c, on plotting a graph between 1/u and 1/v, you will get a straight line with slope (–1) and intercept 1/f on y-axis.
Convex lens, optical bench with uprights, lens holder, two pins, three knitting needle, metre rod, spirit level
1. Fix an upright at 50 cm mark and put lens holder and lens in it.
2. Place the other two uprights holding pins on the optical bench, one on either side of the lens.
3. Level the optical bench with the help of spirit level and levelling screws.
4. Adjust the centre of the lens and the tips of the pins in the same horizontal line.
(A) Determination of bench correction
1. Place the knitting needle along the metre scale. Read the position of its two ends, avoiding error due to parallax. Find the length of the knitting needle l.
2. Adjust the position of the object pin O, so that the distance between the centre of the lens and the tip of the pin is l. Read the position of the lens and the object pin O on the scale of the optical bench. Find the observed length of the knitting needle on the optical bench scale l1.
3. Determine bench correction (l – l1) for the object pin O.
4. Repeat the same procedure for image pin I also and find the bench correction (l – l2) for it.
(B) Determination of approximate focal length of the lens
5. Take out the lens from lens holder and hold it in such a way so that a clear distinct image of a distant object is obtained on the wall.
6. Measure the distance between the lens and the wall with the help of a metre scale.
7. Record the approximate focal length f1 of the lens.
(C) Determination of v for different values of u
8. Fix the lens again in the lens holder on optical bench.
9. Fix the object pin O between f1, and 2f1 with respect to the lens. See from the other side of the lens so that a clear, real, inverted enlarged image of O is formed by the lens.
10. Move the image-pin I, beyond 2f1 and remove parallax between the tip of the image of O and the tip of I by moving your eyes to the left and then to the right side of the image and seeing that the two tips remain in contact as you move your eye. Also observe on other side of the lens that parallax between the tip of pin O and tip of inverted image of pin I has been removed, (i.e. I functions as object).
11. Fix pin I also. Measure the separation between the uprights of L and O (i.e. u) and L and I (i.e. v) on the scale of optical bench.
12. Repeat the steps for different positions of object pin O five or six times. Keep it beyond f1 every time and see that the image formed is inverted.
(D) Plotting the graph and calculation of f
13. Calculate the value of 1/u and 1/v for each observation by taking u and v in metres.
14. Plot graph with 1/u on x-axis and 1/v on y-axis. Take same scale for both axes. Start from zero on either axes. In this graph plot also the points with values of u and v interchanged, because you observed removal of parallax on other side of the lens as well, when pin I functions as object.
15. Read the intercept on any axis. Reciprocal of it gives the focal length.