Answer the following. (i) Draw a ray diagram to show the path of the refracted ray in each of the following cases : A ray of light incident on a concave lens (1) parallel to its principal axis, and (2) is directed towards its principal focus. (ii) A 4 cm tall object is placed perpendicular to the principal axis of convex lens of focal length 24 cm. The distance of object from the lens is 16 cm. Find the position and size of image formed.

ScienceCBSE Class 10 · Board exam 2024, set 31/3/1 · 5 marks · Long answer

CBSE Class 10 Science 2024: question 36(a)

Set in the CBSE Class 10 board exam of 2024, paper 31/3/1, 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)
Draw a ray diagram to show the path of the refracted ray in each of the following cases : A ray of light incident on a concave lens (1) parallel to its principal axis, and (2) is directed towards its principal focus.
0 marks
(ii)
A 4 cm tall object is placed perpendicular to the principal axis of convex lens of focal length 24 cm. The distance of object from the lens is 16 cm. Find the position and size of image formed.
5 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 31/3/1.

Hints

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

Hint 1

A concave lens is diverging. A ray parallel to the axis seems to come from the focus, and the reverse is also true.

Hint 2

Use $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ with u negative and f positive for a convex lens.

Hint 3

For a lens, $m = \frac{h ^{'}}{h} = \frac{v}{u}$ . A negative v means the image is on the object's side.

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)(1) Ray diagram: ray parallel to the principal axis of a concave lens.
- Draw a concave lens with optical centre O, its principal axis, and foci $F_{1}$ (on the object side) and $F_{2}$ .
- Draw a ray, with an arrow, travelling parallel to the principal axis and striking the lens.
- After refraction the ray diverges away from the axis.
- Extend it backwards with a dotted line; the extension passes through $F_{1}$ on the same side as the incoming ray.
- So the refracted ray appears to come from the principal focus $F_{1}$ .
1 mark
(i)(2) Ray diagram: ray directed towards the principal focus of a concave lens.
- Draw a ray, with an arrow, aimed towards $F_{2}$ on the far side of the lens. Show its continuation beyond the lens as a dotted line meeting $F_{2}$ .
- After refraction the ray emerges parallel to the principal axis.
Arrows must be shown on all rays; half a mark is lost if they are missing.
1 mark
(ii) Given (using the sign convention): height of object $h = + 4$ cm, object distance $u = - 16$ cm, focal length of convex lens $f = + 24$ cm.
½ mark
(ii) Lens formula: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$
½ mark
(ii) Substituting:
$\frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{24} + \frac{1}{( - 16 )} = \frac{2 - 3}{48} = - \frac{1}{48}$
$∴ v = - 48 cm$
The image is formed 48 cm from the lens, on the same side as the object. It is virtual and erect.
1 mark
(ii) Magnification: $m = \frac{h ^{'}}{h} = \frac{v}{u}$
½ mark
(ii) Size of image:
$\frac{h ^{'}}{4} = \frac{- 48}{- 16} = 3$
$h^{'} = 3 \times 4 = + 12 cm$
The image is 12 cm tall, erect and magnified 3 times.
½ mark

Answer: (i) (1) refracted ray diverges and appears to come from $F_{1}$ ; (2) refracted ray emerges parallel to the principal axis. (ii) v = −48 cm (on the same side as the object, virtual, erect); image height = 12 cm

Where the marks are

Correct ray diagram for a ray parallel to the principal axis, with arrows (1 mark)
Correct ray diagram for a ray directed towards the focus, with arrows (1 mark)
Writes the given values with correct signs (½ mark)
Writes the lens formula (½ mark)
Calculates v = −48 cm (1 mark)
Writes the magnification formula (½ mark)
Calculates h' = 12 cm (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 paper2024 board paper, set 31/3/1: every question, by section.

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CBSE Class 10 Science 2024: question 36(a)

Hints

Step-by-step solution

Revise the chapter

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