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Light in Class 10 is two things at once: ray diagrams you must draw neatly, and numericals where one wrong sign flips a real image into a virtual one. Students often learn the formulas but lose marks by mixing the mirror and lens versions or forgetting the sign convention. This post sets out the rules, works through one mirror and one lens problem in full, lists the common traps, and ends with a practice routine.
What does the syllabus include?
The CBSE Class X Science syllabus for 2026-27 lists reflection by curved surfaces, images formed by spherical mirrors, the mirror formula ("Derivation not required") and magnification, refraction and its laws, refractive index, images formed by spherical lenses, the lens formula, magnification and power of a lens. Unit III, Natural Phenomena, carries 12 marks and also includes the human eye chapter. Two practicals come from here: finding the focal length of a concave mirror and a convex lens, and tracing a ray through a glass slab. The formulas below follow Chapter 9 of the NCERT Class 10 Science textbook. Check the current syllabus for your year.
How does the sign convention work?
NCERT uses the New Cartesian sign convention:
Place the object to the left of the mirror or lens, so light travels left to right.
Measure all distances from the pole (mirror) or optical centre (lens).
Distances in the direction of incident light are positive; distances against it are negative.
Heights above the principal axis are positive; below, negative.
So the object distance u is always negative in these problems. A concave mirror has a negative focal length; a convex mirror, positive. A convex lens has a positive focal length; a concave lens, negative.
The formulas:
Mirror: 1/v + 1/u = 1/f, and magnification m = h′/h = −v/u.
Lens: 1/v − 1/u = 1/f, and m = h′/h = v/u.
Power of a lens: P = 1/f, with f in metres. The unit is the dioptre (D).
Refractive index: n = speed of light in air ÷ speed in the medium.
A worked mirror problem
Problem. An object is 15 cm in front of a concave mirror of focal length 10 cm. Find the image position and nature.
Signs: u = −15 cm, f = −10 cm.
1/v = 1/f − 1/u = −1/10 + 1/15 = (−3 + 2)/30 = −1/30. So v = −30 cm.
m = −v/u = −(−30)/(−15) = −2.
The image is 30 cm in front of the mirror (negative v, same side as the object), so it is real. The magnification −2 means it is inverted and twice the object's size. This matches the ray diagram: an object between F and C gives a real, inverted, enlarged image beyond C.
A worked lens problem
Problem. A 4 cm tall object is placed 25 cm from a convex lens of focal length 15 cm. Find the image position, size and the power of the lens.
Signs: u = −25 cm, f = +15 cm.
1/v = 1/f + 1/u = 1/15 − 1/25 = (5 − 3)/75 = 2/75. So v = +37.5 cm.
m = v/u = 37.5/(−25) = −1.5. Image height h′ = −1.5 × 4 = −6 cm.
Power: f = 0.15 m, so P = 1/0.15 ≈ +6.7 D.
The image is 37.5 cm on the far side of the lens, real, inverted and 6 cm tall. Again, the ray diagram agrees: an object between F and 2F gives an enlarged image beyond 2F.
A refraction check. NCERT gives the refractive index of a glass as 1.50 in one exercise. Light's speed in that glass is 3 × 10⁸ ÷ 1.5 = 2 × 10⁸ m/s.
Which mistakes cost the most marks?
Using the mirror formula for a lens. Mirrors add (1/v + 1/u), lenses subtract (1/v − 1/u).
Wrong magnification formula. For mirrors m = −v/u; for lenses m = v/u.
Leaving f in centimetres for power. A 15 cm lens has power 1/0.15, not 1/15.
Dropping the sign of u. The object distance is negative in these problems.
Ray diagrams without arrows. Rays need arrowheads, and virtual rays should be dashed.
The deeper issue is that the formula and the picture are learned separately. Goldberg and McDermott (1987) interviewed university students about real lenses and mirrors and found that many who had just completed geometrical optics could not relate the ray-tracing they had learned to an actual lens, object and screen, and had trouble drawing and reading ray diagrams. In Class 10, pairing every numerical with a rough diagram is how you build that link.
A practice routine for this chapter
Day 1: Draw the six concave-mirror ray diagrams (object at infinity, beyond C, at C, between C and F, at F, between F and P) from memory.
Day 2: Do the same for the convex lens.
Day 3: Solve six numericals, three mirror and three lens. For each, write the signs first and sketch a diagram to check.
Day 4: Five power and refractive index questions.
If you want to see the image move as you slide the object, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read. For the habit of sketching before solving, read our post on drawing the diagram first.
Tonight, solve one mirror and one lens problem, writing every sign before you calculate.
