The variation of image distance (v) with object distance (u) for a convex lens is given in the following observation table. Analyse it and answer the questions that follow : S. No. Object distance (u) cm Image distance (v) cm --- --- --- 1 -150 +30 2 -75 +37.5 3 -50 +50 4 -37.5 +75 5 -30 +150 6 -15 +37.5 (i) Without calculation, find the focal length of the convex lens. Justify your answer. (ii) Which observation is not correct ? Why ? Draw ray diagram to find the position of the image formed for this position of the object. (iii) Find the approximate value of magnification for u = -30 cm.

ScienceCBSE Class 10 · Board exam 2024, set 31/4/1 · 5 marks · Long answer

CBSE Class 10 Science 2024: question 36(a)

Set in the CBSE Class 10 board exam of 2024, paper 31/4/1, 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 answerCompetency-basedLight – Reflection and Refraction

The variation of image distance (v) with object distance (u) for a convex lens is given in the following observation table. Analyse it and answer the questions that follow :

S. No.	Object distance (u) cm	Image distance (v) cm
1	$- 150$	$+ 30$
2	$- 75$	$+ 37.5$
3	$- 50$	$+ 50$
4	$- 37.5$	$+ 75$
5	$- 30$	$+ 150$
6	$- 15$	$+ 37.5$

(i) Without calculation, find the focal length of the convex lens. Justify your answer.
(ii) Which observation is not correct ? Why ? Draw ray diagram to find the position of the image formed for this position of the object.
(iii) Find the approximate value of magnification for $u = - 30$ cm.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 31/4/1.

Hints

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

Hint 1

Look for the row where the object distance and the image distance have the same size. Where is the object placed for a convex lens in that case?

Hint 2

For the incorrect row, compare u with the focal length you found. Is the object inside F? What kind of image forms then, and which sign should v have?

Hint 3

Magnification for a lens is m = v/u. Use the values in the row with u = −30 cm.

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) In observation S. No. 3, $u = - 50$ cm and $v = + 50$ cm. The object distance and the image distance are equal in size, which happens only when the object is at $2 F_{1}$ ; the image then forms at $2 F_{2}$ .
1 mark
(i) So $2 f = 50$ cm, giving focal length $f = 25$ cm.
1 mark
(ii) Observation S. No. 6 ( $u = - 15$ cm, $v = + 37.5$ cm) is not correct.
½ mark
(ii) Reason: $u = 15$ cm is less than $f = 25$ cm, so the object lies between $F_{1}$ and the optical centre $O$ . The image is then virtual, erect and on the same side as the object, so $v$ must be negative. Check: $\frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{25} - \frac{1}{15} = - \frac{2}{75}$ , so $v = - 37.5$ cm.
½ mark
(ii) Ray diagram, described in words:
- Draw a convex lens with its principal axis, and mark $F_{1}$ and $F_{2}$ at 25 cm on either side of $O$ .
- Place the object AB upright at 15 cm from $O$ , between $F_{1}$ and $O$ .
- Ray 1 leaves B parallel to the principal axis and, after refraction, passes through $F_{2}$ .
- Ray 2 leaves B, passes through $O$ and goes on undeviated.
- The two refracted rays diverge, so produce them backwards as dotted lines. They meet at B′ on the object side, at about 37.5 cm from the lens.
- A′B′ is virtual, erect and enlarged.
- Show arrowheads on all rays; ½ mark is deducted if ray directions are missing.
1 mark
(iii) For S. No. 5: $m = \frac{v}{u} = \frac{+ 150 cm}{- 30 cm} = - 5$ . The image is real, inverted and 5 times the size of the object.
1 mark

Answer: (i) f = 25 cm (u = v = 50 cm ⇒ object at 2F); (ii) S. No. 6 is wrong – object inside F gives a virtual image, v ≈ −37.5 cm; (iii) m = −5

Where the marks are

Identifies S. No. 3 and gets f = 25 cm (1 mark)
Justifies: u = v means the object is at 2F (1 mark)
Identifies S. No. 6 as incorrect (½ mark)
Reason: v should be negative because the image forms on the same side as the object (½ mark)
Correct ray diagram with arrows for an object between F and O (1 mark)
m = v/u = 150/(−30) = −5 (1 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 paper2024 board paper, set 31/4/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Science 2024: question 36(a)

Hints

Step-by-step solution

Revise the chapter

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