ScienceCBSE Class 10 · Board exam 2023, set 31/4/1 · 3 marks · Short answer

CBSE Class 10 Science 2023: question 30(B)

Set in the CBSE Class 10 board exam of 2023, paper 31/4/1, section C, question 30(B), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(B) · 3 marks · Short answerLight – Reflection and Refraction

An object of height 10 cm is placed 25 cm away from the optical centre of a converging lens of focal length 15 cm. Calculate the image-distance and height of the image formed.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 31/4/1.

Hints

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

Hint 1

Use the New Cartesian sign convention: object distance is negative and f of a convex lens is positive.

Hint 2

Apply $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ to find v first.

Hint 3

For a lens, $m = \frac{v}{u} = \frac{h ^{'}}{h}$ .

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.

Given: $h = + 10$ cm, $u = - 25$ cm, $f = + 15$ cm (converging lens).
Lens formula: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ , so $\frac{1}{v} = \frac{1}{f} + \frac{1}{u}$
½ mark
$\frac{1}{v} = \frac{1}{15} + \frac{1}{- 25} = \frac{5 - 3}{75} = \frac{2}{75}$
½ mark
$v = \frac{75}{2} = + 37.5$ cm. The image is formed 37.5 cm on the other side of the lens.
½ mark
Magnification: $m = \frac{h ^{'}}{h} = \frac{v}{u}$ , so $h^{'} = h \times \frac{v}{u}$
½ mark
$h^{'} = 10 \times \frac{37.5}{- 25}$
½ mark
$h^{'} = - 15$ cm. The image is 15 cm tall; the negative sign shows it is real and inverted.
½ mark

Answer: v = +37.5 cm; h' = −15 cm (real, inverted, 15 cm tall)

Where the marks are

Writes lens formula (½ mark)
Correct substitution with signs (½ mark)
v = 37.5 cm (½ mark)
Magnification relation $h^{'} / h = v / u$ (½ mark)
Substitution (½ mark)
h' = −15 cm (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 paper2023 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 2023: question 30(B)

Hints

Step-by-step solution

Revise the chapter

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