Answer the following. (a) Upper half of a convex lens is covered with a black paper. Draw a ray diagram to show the formation of image of an object placed at a distance of 2F from such a lens. Mention the position and nature of the image formed. State the observable difference in the image obtained if the lens is uncovered. Give reason to justify your answer. (b) An object is placed at a distance of 30 cm from the optical centre of a concave lens of focal length 15 cm. Use lens formula to determine the distance of the image from the optical centre of the lens.

ScienceCBSE Class 10 · Board exam 2024, set 31/2/1 · 5 marks · Long answer

CBSE Class 10 Science 2024: question 36

Set in the CBSE Class 10 board exam of 2024, 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

Answer the following.

(a)
Upper half of a convex lens is covered with a black paper. Draw a ray diagram to show the formation of image of an object placed at a distance of 2F from such a lens. Mention the position and nature of the image formed. State the observable difference in the image obtained if the lens is uncovered. Give reason to justify your answer.
0 marks
(b)
An object is placed at a distance of 30 cm from the optical centre of a concave lens of focal length 15 cm. Use lens formula to determine the distance of the image from the optical centre of the lens.
0 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 31/2/1.

Hints

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

Hint 1

Every part of a lens forms a complete image. Covering part of the lens only changes how much light reaches the image.

Hint 2

For a concave lens, the focal length is negative. Use 1/v − 1/u = 1/f.

Hint 3

1/v = 1/(−15) + 1/(−30). Simplify the fraction.

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:
- Draw the principal axis with a convex lens at O and the upper half shaded black. Mark $F_{1}$ , $2 F_{1}$ on the left and $F_{2}$ , $2 F_{2}$ on the right.
- Place an upright object AB at $2 F_{1}$ .
- Ray 1: from the top B, passing through $F_{1}$ and striking the uncovered lower half. It emerges parallel to the principal axis.
- Ray 2: from B, directed at the optical centre O, just below the black paper. It goes straight on undeviated.
- The two rays meet below the axis at $2 F_{2}$ . Draw the inverted image A′B′ there. Mark arrows on all rays.
1 mark
(a) Position of image: at $2 F_{2}$ , on the other side of the lens.
½ mark
(a) Nature of image: real, inverted and of the same size as the object. Covering half the lens does not cut off half the image; the full image still forms.
½ mark
(a) Observable difference when the lens is uncovered: the image forms at the same place with the same size, but it is brighter.
½ mark
(a) Reason: with the whole lens uncovered, more rays from the object pass through the lens and meet at the image. More light reaches the image, so it is brighter.
½ mark
(b) Given (sign convention, light from left): object distance $u = - 30$ cm; focal length of the concave lens $f = - 15$ cm; image distance $v = ?$
½ mark
Lens formula: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{v} = \frac{1}{f} + \frac{1}{u}$
½ mark
Substituting: $\frac{1}{v} = \frac{1}{- 15} + \frac{1}{- 30} = \frac{- 2 - 1}{30} = - \frac{1}{10}$ So $v = - 10$ cm. The image is 10 cm from the optical centre, on the same side as the object. It is virtual and erect.
1 mark

Answer: (a) Image at 2F₂ on the other side, real, inverted, same size; it becomes brighter when the lens is uncovered because more rays pass through. (b) v = −10 cm (10 cm from the optical centre, same side as the object)

Where the marks are

Correct ray diagram using the uncovered half, with arrows (1 mark)
Image at 2F on the other side (½ mark)
Real and inverted (½ mark)
Image becomes brighter when uncovered (½ mark)
Reason: more rays pass through the lens (½ mark)
Writes the given values with signs (½ mark)
Writes the lens formula (½ mark)
Gets v = −10 cm (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 paper2024 board paper, set 31/2/1: every question, by section.

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CBSE Class 10 Science 2024: question 36

Hints

Step-by-step solution

Revise the chapter

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