Answer the following. (i) The power of a lens 'X' is -2.5 D. Name the lens and determine its focal length in cm. For which eye defect of vision will an optician prescribe this type of lens as a corrective lens? (ii) "The value of magnification 'm' for a lens is -2." Using new Cartesian Sign Convention and considering that an object is placed at a distance of 20 cm from the optical centre of this lens, state: (I) the nature of the image formed; (II) size of the image compared to the size of the object; (III) position of the image, and (IV) sign of the height of the image. (iii) The numerical values of the focal lengths of two lenses A and B are 10 cm and 20 cm respectively. Which one of the two will show higher degree of convergence/divergence? Give reason to justify your answer.

ScienceCBSE Class 10 · Board exam 2025, set 31/1/1 · 5 marks · Long answer

CBSE Class 10 Science 2025: question 36(a)

Set in the CBSE Class 10 board exam of 2025, paper 31/1/1, section D, question 36(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q36(a) · 5 marks · Long answerLight – Reflection and Refraction

Answer the following.

(i)
The power of a lens 'X' is $- 2.5$ D. Name the lens and determine its focal length in cm. For which eye defect of vision will an optician prescribe this type of lens as a corrective lens?
0 marks
(ii)
"The value of magnification 'm' for a lens is $- 2$ ." Using new Cartesian Sign Convention and considering that an object is placed at a distance of 20 cm from the optical centre of this lens, state: (I) the nature of the image formed; (II) size of the image compared to the size of the object; (III) position of the image, and (IV) sign of the height of the image.
0 marks
(iii)
The numerical values of the focal lengths of two lenses A and B are 10 cm and 20 cm respectively. Which one of the two will show higher degree of convergence/divergence? Give reason to justify your answer.
0 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 31/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

The sign of the power tells you the type of lens; remember to convert metres to cm.

Hint 2

A negative m means an inverted image; use m = v/u to find v.

Hint 3

Power and focal length are reciprocals of each other.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(i) The power is negative, so lens X is a concave (diverging) lens.
½ mark
Use $P = \frac{1}{f ( in m )}$ , so $- 2.5 = \frac{1}{f}$ .
½ mark
$f = \frac{1}{- 2.5} m = - 0.4 m = - 40 cm$ .
½ mark
A concave lens corrects myopia (short-sightedness / near-sightedness).
½ mark
(ii) Here $m = - 2$ and $u = - 20$ cm. Since $m = \frac{v}{u}$ , we get $v = m u = (- 2) (- 20) = + 40$ cm. A negative magnification means the image is inverted, so the lens is convex.
(I) Nature: real and inverted, because $m$ is negative.
½ mark
(II) Size: magnified, twice the size of the object, since $∣ m ∣ = 2$ .
½ mark
(III) Position: $v = + 40$ cm, i.e. 40 cm on the other side of the lens. Here $\frac{1}{f} = \frac{1}{40} + \frac{1}{20}$ , so $f \approx 13.3$ cm and $2 F \approx 26.7$ cm. The image is therefore **beyond $2 F_{2}$ **.
½ mark
(IV) Sign of image height: negative, because the image is inverted and lies below the principal axis.
½ mark
(iii) Lens A (focal length 10 cm) shows the higher degree of convergence or divergence.
½ mark
Reason: $P = \frac{1}{f}$ , so the shorter the focal length, the greater the power. $P_{A} = \frac{100}{10} = 10$ D, while $P_{B} = \frac{100}{20} = 5$ D in magnitude.
½ mark

Answer: (i) Concave lens, f = −40 cm, corrects myopia; (ii) (I) real and inverted, (II) magnified – twice the object size, (III) 40 cm on the other side of the lens (beyond 2F), (IV) negative; (iii) Lens A (10 cm), because smaller focal length means greater power.

Where the marks are

Names lens as concave (½ mark)
Uses P = 1/f (½ mark)
Gets f = −40 cm (½ mark)
Names myopia (½ mark)
Image real and inverted (½ mark)
Image magnified/double size (½ mark)
Image on other side, beyond 2F (½ mark)
Height negative (½ mark)
Chooses lens A (½ mark)
Reason: less focal length, more power (½ mark)

Revise the chapter

Chapter: Light – Reflection and Refraction (notes, formulas, where marks are lost and every past question)
Topic: Lens Formula, Magnification and Power of a Lens

Practise this chapterBoard-style questions from Light – Reflection and Refraction, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 31/1/1: every question, by section.

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CBSE Class 10 Science 2025: question 36(a)

Hints

Step-by-step solution

Revise the chapter

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