ScienceCBSE Class 10 · Board exam 2023, set 31/2/1 · 5 marks · Long answer

CBSE Class 10 Science 2023: question 36

Set in the CBSE Class 10 board exam of 2023, paper 31/2/1, section D, question 36, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q36 · 5 marks · Long answerLight – Reflection and Refraction

(a) An object is placed in front of a convex lens of focal length f. If the distance of the object from the lens is 2f, draw a ray diagram to show the formation of the image. Write the value of magnification in this case.
(b) A student has focussed the image of a candle flame on a white screen using a convex lens. The situation is as given below: Length of the flame = 2 cm; Focal length of the lens = 12 cm; Distance of the flame from the lens = 16 cm. If the flame is perpendicular to the principal axis of the lens, calculate the values of the following :
(i) Distance of the image from the lens
(ii) Length of the image formed

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

For (a), use two rays: one parallel to the axis and one through the optical centre.

Hint 2

For a convex lens, f is positive and the object distance u is negative.

Hint 3

Use 1/v − 1/u = 1/f, then m = v/u = 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.

(a) Ray diagram in words: draw the principal axis and the convex lens, and mark F₁, 2F₁ on the left and F₂, 2F₂ on the right. Place object AB upright at 2F₁. Ray 1 from A runs parallel to the principal axis and, after refraction, passes through F₂. Ray 2 from A passes through the optical centre O without deviation. The two rays meet at A′ below the axis at 2F₂. Draw the image A′B′ at 2F₂, with arrows on all rays. The image is real, inverted and the same size as the object.
1½ marks
Since the image is the same size and inverted, the magnification is $m = - 1$ .
½ mark
(b) Data: $h = + 2$ cm, $f = + 12$ cm, $u = - 16$ cm. Lens formula: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$
½ mark
(i) $\frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{12} + \frac{1}{- 16} = \frac{4 - 3}{48}$
½ mark
$\frac{1}{v} = \frac{1}{48}$ , so $v = + 48$ cm. The image is 48 cm from the lens, on the side opposite to the flame.
½ mark
(ii) Magnification: $m = \frac{h ^{'}}{h} = \frac{v}{u}$ , so $h^{'} = h \times \frac{v}{u}$
½ mark
$h^{'} = 2 cm \times \frac{48}{- 16}$
½ mark
$h^{'} = - 6$ cm. The image is 6 cm long, real and inverted.
½ mark

Answer: (a) Image at 2F₂: real, inverted, same size; m = −1. (b)(i) v = +48 cm; (ii) image length = 6 cm (h′ = −6 cm, inverted).

Where the marks are

Correct ray diagram with object at 2F₁ and image at 2F₂, arrows shown (1½ marks; ½ deducted if arrows missing)
Magnification = −1 (½ mark)
Correct sign convention and lens formula (½ mark)
Correct substitution (½ mark)
v = +48 cm (½ mark)
Magnification formula h′ = hv/u (½ mark)
Correct substitution (½ mark)
h′ = −6 cm, i.e. image 6 cm long (½ mark)

Revise the chapter

Chapter: Light – Reflection and Refraction (notes, formulas, where marks are lost and every past question)

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.

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 36

Hints

Step-by-step solution

Revise the chapter

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