Convex lens table: u = −50, v = +50, so f = 50 cm? Find f and the wrong reading | Class 10 Light

Board question (CBSE 2026 Main, 31/3/1 Q38 (a), (b)): The variation of image distance (v) with the object distance (u) for a convex lens is given in the following observation table. Analyse it and answer the questions given below: u (cm) −150, −75, −50, −37.5, −30, −15; v (cm) +30, +37.5, +50, +75, +150, +37.5. (a) Without calculation, find out the focal length of the given convex lens. Justify your answer. (b) Which one of the observations given in the table is not correct and why?

A convex lens table shows u = −50 cm and v = +50 cm. Is f 50 cm? No. Object distance equals image distance only at 2F, so 2F = 50 cm and f = 25 cm. Then find the reading that cannot be right: for u = −15 cm the object is between F and the lens, the image is on the same side, and v must be negative. Solve the board question the way the marking scheme wants it.

Question (CBSE board question, case-based): The variation of image distance (v) with the object distance (u) for a convex lens is given in an observation table: u = −150, −75, −50, −37.5, −30, −15 cm; v = +30, +37.5, +50, +75, +150, +37.5 cm. (a) Without calculation, find out the focal length of the given convex lens. Justify your answer. (b) Which one of the observations given in the table is not correct and why?
(a) Observation 3: u = −50 cm, v = +50 cm. Same distance (|u| = |v|) only at 2F, so 2F = 50 cm and f = 25 cm.
(b) Observation 6: u = −15 cm is between F and the lens. Lens formula 1/v − 1/u = 1/f → 1/v = 1/25 − 1/15 = −2/75 → v = −37.5 cm: the image is virtual, on the same side as the object. The table gives +37.5 cm, so observation 6 is wrong.

Marking scheme value points (CBSE 2026 Main 31/3/1 Q38, parts (a) and (b), 2 marks): (a) observation 3, object distance = image distance, only possible at 2F = 50 cm, so f = 25 cm (1) · (b) observation 6 (½) · object between F and O, so the image is on the same side as the object and v should be negative (½). The lens-formula line is the check, not a scheme step.
The trap: reading f straight off the same-distance row gives f = 50 cm. That row is 2F; halve it.
Memory hook (convex lens): same distance for u and v? That is 2F: halve it for the focal length.
Repeats: this table (the same six u, v readings) came in 5 CBSE board papers: 2024 Main 31/4/1 Q36(a) and 31/4/2 Q35(a), and 2026 Main 31/3/1 Q38, 31/3/2 Q38 and 31/3/3 Q38.

Comment challenge (CBSE 2026 Main 31/1/1 Q30, also 31/1/2 Q31 and 31/1/3 Q30, 1 mark): a convex lens of focal length 15 cm forms a real image of the same size. Where are the object and the image? (A) −15 cm and −15 cm (B) −15 cm and +15 cm (C) −30 cm and +30 cm (D) −30 cm and −30 cm. Answer in the pinned comment.
Quick recall (Light, magnification sign, single lens or mirror, real object): m is negative: image? → Real, inverted

References: NCERT Class 10 Science, Ch 9 Light – Reflection and Refraction (image formation by a convex lens, object at 2F1 gives a real, inverted, same-size image at 2F2, and an object between F1 and O gives a virtual, erect image on the same side; New Cartesian sign convention; lens formula 1/v − 1/u = 1/f; magnification m = h′/h = v/u, §9.3); CBSE Class 10 board questions and marking schemes.

Narration uses a licensed AI voice (Azure AI Speech, Indian English). Script and physics research by ScoreSpark.

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