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The convex lens experiment is one of the most common optics practicals in the CBSE Class 12 board exam, and it is easy to lose marks on the recording, not the physics. This post walks through the method in the NCERT lab manual. It works a full set of sample readings, covers both graphs and the error in f, and shows the calculation slip that quietly shifts your answer.
Is this experiment in your syllabus?
The CBSE Physics curriculum for 2026-27 lists, in Section B of the Class 12 practicals: "To find the focal length of a convex lens by plotting graphs between u and v or between 1/u and 1/v." The JEE Main 2026 syllabus includes the focal length of a convex lens among its experimental skills, using the parallax method, so the same set-up appears there too. The full procedure is Experiment 10 of the NCERT Class 12 physics laboratory manual.
What is the principle?
For a thin convex lens forming a real image, the lens formula with the new Cartesian sign convention is 1/f = 1/v − 1/u, with u negative. The lab manual rewrites it for the positive distances you actually measure on the bench:
1/f = 1/v + 1/u, so f = uv/(u + v)
When u = v, each equals 2f, and u and v are interchangeable. The manual therefore asks you to keep the object between f and 2f. As u moves from 2f to f, v moves from 2f towards infinity.
How do you set up and take readings?
Find a rough f by focusing a distant object, such as a tree, onto a sheet of paper. Never look at the Sun through the lens.
Level the optical bench and mount the lens near the middle, with the pin tips at the height of the lens centre.
Find the index correction with a knitting needle. The true distance from the pin tip to the optical centre is the needle's length plus half the lens thickness. The difference between this and the bench reading is the correction, which you add to every observed u and v.
Put the object pin just inside 2f. Move the image pin until it and the inverted image show no parallax: tip touches tip and they move together as you shift your eye.
Record the positions, move the object 2 to 3 cm closer to the lens and repeat for at least six readings.
A worked set of readings
These are sample numbers for a lens of focal length close to 15 cm, after index correction:
u = 20.0 cm, v = 60.5 cm, f = (20.0 × 60.5)/80.5 = 15.03 cm
u = 22.0 cm, v = 46.8 cm, f = 1029.6/68.8 = 14.97 cm
u = 24.0 cm, v = 40.2 cm, f = 964.8/64.2 = 15.03 cm
u = 26.0 cm, v = 35.6 cm, f = 925.6/61.6 = 15.03 cm
u = 28.0 cm, v = 32.2 cm, f = 901.6/60.2 = 14.98 cm
u = 30.0 cm, v = 30.1 cm, f = 903.0/60.1 = 15.02 cm
The mean is (15.03 + 14.97 + 15.03 + 15.03 + 14.98 + 15.02)/6 = 90.06/6 = 15.01 cm.
The error. The manual gives Δf = f²(Δu/u² + Δv/v²). With a least count of 0.1 cm, the first reading gives Δf = 15.03² × (0.1/400 + 0.1/3660) = 225.9 × 0.000277 = 0.06 cm. The others come out a little smaller, and the manual asks you to report the largest. So the result is f = 15.01 ± 0.06 cm.
How do the two graphs give f?
u against v. Use the same scale on both axes. Each pair gives two points, because u and v can be swapped, so six readings give twelve points. The curve is a hyperbola. Draw the line at 45° through the origin. Where it cuts the curve, u = v = 2f. With the sample data, the point (30.0, 30.1) lies almost on that line, so 2f ≈ 30 cm and f ≈ 15 cm.
1/u against 1/v. This is a straight line, and both intercepts equal 1/f. For f = 15 cm, each intercept should be close to 1/15 = 0.0667 cm⁻¹. The manual takes f as 2 divided by the sum of the two intercepts. It also warns that unequal scales stop the line from sitting at 45° and make it harder to read.
Why is this harder than it looks?
Goldberg and McDermott (1987) interviewed university students about a real lens, an object and a screen. Even students who had just finished geometrical optics often could not connect the ray diagrams they had learned to the actual equipment in front of them. Many did not understand what the lens or the screen was doing. On the bench, that shows up as hunting for an image in the wrong place. Before you take readings, sketch a quick ray diagram for u between f and 2f, so you know the image should be real, inverted, magnified and beyond 2f.
Common mistakes and how to avoid them
Skipping the index correction. Every u and v is then off by the same amount.
Pin tips at different heights from the lens centre, so you cannot remove parallax cleanly.
Swapping the object and image pins partway through, which changes their index corrections. The manual warns against it.
Overlapping the tips instead of making them touch tip to tip.
Averaging u and v before calculating f.
A practice routine before the practical exam
Redo the sample calculation above by hand, including Δf, until it takes under ten minutes.
Draw both graphs from the sample readings on graph paper with equal scales.
Answer the self-assessment questions at the end of the manual's experiment aloud, as you would in a viva, such as how f changes when the lens is dipped in water.
Read our guide to ray optics sign conventions and lens formula mistakes and our post on the board practical exam and viva.
If you want to see how v swings as u moves from 2f towards f before you go into the lab, the Fermi Simulation Lab has interactive simulations for the ideas that are easier to see than to read.
Before your next lab session, write out the observation table with columns for the index correction, so you only fill in numbers on the day.
