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The concave mirror experiment shares its formula with the convex lens practical, but the mirror brings its own problems. The image forms on the same side as the object, the pins have to sit at the height of the mirror's pole, and a back-silvered mirror can give double images. This post covers the procedure, works a full set of sample readings, uses a graph the lens post does not, and lists the error sources specific to mirrors.
Which syllabuses include it?
The CBSE Physics curriculum for 2026-27 lists, as experiment 1 in Section B of the Class 12 practicals: "To find the value of v for different values of u in case of a concave mirror and to find the focal length." The JEE (Main) 2026 syllabus includes the focal length of a concave mirror, using the parallax method, under Experimental Skills. The JEE (Advanced) 2026 Information Brochure lists the focal length of a concave mirror using the u-v method. Check the documents for your year.
What is the principle?
The NCERT ray optics chapter derives the mirror equation 1/v + 1/u = 1/f with Cartesian signs. For a concave mirror forming a real image, u, v and f are all negative, so with the positive distances you measure on the bench the same equation reads:
1/f = 1/u + 1/v, so f = uv/(u + v)
Experiment 9 of the NCERT Class 12 physics lab manual uses a mirror of focal length less than 20 cm. With the object between F and C (that is, between f and 2f), the image is real, inverted and magnified, and forms beyond C, where a pin can find it easily.
How do you take readings?
From the lab manual:
Get a rough f by focusing a distant tree or building onto paper. Never look at the Sun's image.
Level the optical bench. Set the object and image pin tips at the height of the mirror's pole.
Find the index correction for each pin with a knitting needle: the needle's true length minus the distance read off the bench scale. Add it to every observed u and v.
Place the object pin near 2F, where an inverted image of the same size appears. Then move it between F and 2F.
Move the image pin until it shows no parallax with the image: tip touching tip, moving together as you shift your eye.
Repeat for at least five or six object positions, and calculate f for each.
A worked set of readings
Sample numbers after index correction, for a mirror with f close to 12 cm:
u = 15.0 cm, v = 60.2 cm: f = 903.0/75.2 = 12.01 cm
u = 17.0 cm, v = 40.7 cm: f = 691.9/57.7 = 11.99 cm
u = 19.0 cm, v = 32.7 cm: f = 621.3/51.7 = 12.02 cm
u = 21.0 cm, v = 27.9 cm: f = 585.9/48.9 = 11.98 cm
u = 23.0 cm, v = 25.2 cm: f = 579.6/48.2 = 12.02 cm
u = 24.0 cm, v = 24.0 cm: f = 576.0/48.0 = 12.00 cm
Mean f = 72.02/6 = 12.00 cm.
The error. The manual gives Δf = f²(Δu/u² + Δv/v²) and asks you to report the largest value. With 0.1 cm in each distance, the first reading gives 12.01² × (0.1/225 + 0.1/3624) = 144.2 × 0.000472 = 0.07 cm. So f = 12.00 ± 0.07 cm.
Which graphs give f?
u against v. Use equal scales. The curve is a hyperbola. Draw the 45 degree line through the origin; it cuts the curve where u = v = 2f. In the sample, (24.0, 24.0) lies on that line, so 2f = 24 cm and f = 12 cm. That reading is the object at C, where the image falls back on the object itself.
uv against (u + v). The manual suggests this as an extra activity. Since uv = f(u + v), the graph is a straight line through the origin with slope f. For the sample data, the best line has slope 12.01 cm. It is a good check because every reading contributes to one slope.
What sources of error are specific to mirrors?
The manual's precautions and sources of error:
Back-silvered mirrors. The glass in front of the silvering gives extra reflections. A front-coated mirror avoids this.
Large aperture. Rays far from the axis do not meet at one point, so the image is blurred. Keep the aperture small.
Heights not matched. If the pin tips and the pole are not at one level, or the bench is not horizontal, parallax will not clear properly.
Swapped pins. The object and image pins have different index corrections. Do not interchange them.
Averaging u and v. Calculate f for each pair, then average. With the sample data, mean u and mean v give 12.67 cm, which is badly off.
Can you use an object closer than F? The image is then virtual and behind the mirror, where a pin in front cannot locate it by parallax, so this method fails. The manual asks this as a self-assessment question.
For the lens version of the experiment, with the 1/u against 1/v graph, see our post on the convex lens focal length experiment. For sign-convention slips in problems, see ray optics mistakes.
A practice routine
Recompute f for each sample reading and the error for the first one.
Plot uv against (u + v) and find the slope.
Sketch the ray diagram for an object between F and C, so you know where to look for the image before you start.
Practise explaining index correction and parallax in one sentence each.
To see how the image moves as the object crosses F and C, the Fermi Simulation Lab has interactive simulations for ideas easier to see than read.
Before your lab session, draw the uv against (u + v) graph from these sample readings and check that the slope comes out near 12 cm.
