The above image shows a thin lens of focal length 5 m. (i) What is the kind of lens shown in the above figure? (ii) If a real inverted image is to be formed by this lens at a distance of 7 m from the optical centre, then show with calculation where should the object be placed? (iii) Draw a neatly labelled diagram of the image formation mentioned in (ii).

ScienceCBSE Class 10 · Sample paper, session 2023-24 · 5 marks · Long answer

CBSE Class 10 Science sample paper 2023-24: question 36(a)

From the official CBSE sample question paper for 2023-24, 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

The above image shows a thin lens of focal length 5 m.

(i)
What is the kind of lens shown in the above figure?
1 mark
(ii)
If a real inverted image is to be formed by this lens at a distance of 7 m from the optical centre, then show with calculation where should the object be placed?
2 marks
(iii)
Draw a neatly labelled diagram of the image formation mentioned in (ii).
2 marks

Figure in the paper: A thin convex (double convex) lens drawn on a horizontal principal axis, with two focal points marked on the axis on either side of the lens: F2 on the left and F1 on the right, labelled 'principal axis'. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Look at the shape: is the lens thicker at the centre or at the edges?

Hint 2

Use $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ . A real image from a convex lens forms on the other side, so take $v$ as positive.

Hint 3

For the diagram, compare your object distance with $2 f = 10$ m, then draw a ray parallel to the axis and a ray through the optical centre.

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) The lens in the figure is thicker at the middle than at the edges. It has focal points on both sides of the principal axis. It is a convex (converging) lens.
1 mark
(ii) Use the lens formula $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ with the New Cartesian sign convention.
For a convex lens $f = + 5 m$ . A real image forms on the other side of the lens, so $v = + 7 m$ .
½ mark
Substituting: $\frac{1}{5} = \frac{1}{7} - \frac{1}{u}$
½ mark
$\frac{1}{u} = \frac{1}{7} - \frac{1}{5} = \frac{5 - 7}{35} = - \frac{2}{35}$
½ mark
$u = - \frac{35}{2} = - 17.5 m$
The object must be placed 17.5 m from the optical centre, on the left side (the side opposite to the image). Since $2 f = 10$ m, the object is beyond $2 F_{2}$ .
½ mark
(iii) Ray diagram (described): Draw the principal axis and the convex lens with $F_{1}$ , $2 F_{1}$ on the right and $F_{2}$ , $2 F_{2}$ on the left. Place object AB upright at 17.5 m on the left, beyond $2 F_{2}$ .
- Ray 1 from A, parallel to the principal axis, refracts and passes through $F_{1}$ .
- Ray 2 from A passes through the optical centre O without deviation.
1 mark
The two refracted rays meet at A′ below the axis, between $F_{1}$ and $2 F_{1}$ (at 7 m). Draw A′B′ perpendicular to the axis. The image is real, inverted and diminished. Show arrows on all rays.
1 mark

Answer: (i) Convex lens. (ii) $u = - 17.5$ m: object 17.5 m on the left of the lens (beyond $2 F$ ). (iii) Ray diagram with object beyond $2 F_{2}$ and a real, inverted, diminished image between $F_{1}$ and $2 F_{1}$ .

Where the marks are

Identifies the lens as convex (1 mark)
Writes the lens formula with correct signs $f = + 5$ m, $v = + 7$ m (0.5 mark)
Substitutes correctly (0.5 mark)
Obtains $1/ u = - 2/35$ (0.5 mark)
Gets $u = - 17.5$ m and states the object position (0.5 mark)
Ray diagram: object beyond $2 F$ , two correct rays (1 mark)
Arrows shown and real inverted image correctly located (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 paperSample paper 2023-24: 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 sample paper 2023-24: question 36(a)

Hints

Step-by-step solution

Revise the chapter

More questions from Light – Reflection and Refraction