ScienceCBSE Class 10 · Board exam 2023, set 31/2/1 · 3 marks · Short answer

CBSE Class 10 Science 2023: question 31(a)

Set in the CBSE Class 10 board exam of 2023, paper 31/2/1, section C, question 31(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31(a) · 3 marks · Short answerLight – Reflection and Refraction

A student has focussed the image of an object of height 3 cm on a white screen using a concave mirror of focal length 12 cm. If the distance of the object from the mirror is 18 cm, find the values of the following :

(i)
Distance of the image from the mirror
1 mark
(ii)
Height of the image
1 mark

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 31/2/1.

Hints

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

Hint 1

Use the sign convention: distances measured against incident light are negative, and a concave mirror has negative f.

Hint 2

Apply 1/v + 1/u = 1/f and solve for v.

Hint 3

Then use h′/h = −v/u to find the image height.

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 (New Cartesian sign convention): $h = + 3$ cm, $f = - 12$ cm (concave mirror), $u = - 18$ cm.
½ mark
(i) Mirror formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ , so $\frac{1}{v} = \frac{1}{f} - \frac{1}{u}$
½ mark
$\frac{1}{v} = \frac{1}{- 12} - \frac{1}{- 18} = \frac{- 3 + 2}{36} = - \frac{1}{36}$
½ mark
$v = - 36$ cm. The image is 36 cm in front of the mirror, which is where the screen is.
½ mark
(ii) Magnification: $m = \frac{h ^{'}}{h} = - \frac{v}{u}$ , so $h^{'} = - \frac{v}{u} \times h$
½ mark
$h^{'} = - \frac{( - 36 )}{( - 18 )} \times 3 = - 2 \times 3 = - 6$ cm. The image is 6 cm tall, real and inverted.
½ mark

Answer: (i) v = −36 cm (36 cm in front of the mirror); (ii) h′ = −6 cm (6 cm, inverted)

Where the marks are

Correct data with signs (½ mark)
Mirror formula (½ mark)
Correct substitution (½ mark)
v = −36 cm (½ mark)
Magnification formula (½ mark)
h′ = −6 cm (½ mark)

Revise the chapter

Chapter: Light – Reflection and Refraction (notes, formulas, where marks are lost and every past question)
Topic: Mirror Formula, Magnification and Sign Convention

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 31/2/1: every question, by section.

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CBSE Class 10 Science 2023: question 31(a)

Hints

Step-by-step solution

Revise the chapter

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