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The power of a lens is +4D… (Class 10 Science 2023, Q31)

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ScienceCBSE Class 10 · Board exam 2023, set 31/4/1 · 3 marks · Short answer

CBSE Class 10 Science 2023: question 31

Set in the CBSE Class 10 board exam of 2023, paper 31/4/1, section C, question 31, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31 · 3 marks · Short answerLight – Reflection and Refraction

The power of a lens is +4D. Find the focal length of this lens. An object is placed at a distance of 50 cm from the optical centre of this lens. State the nature and magnification of the image formed by the lens and also draw a ray diagram to justify your answer.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 31/4/1.

Hints

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

Hint 1

Power in dioptres is the reciprocal of focal length in metres.

Hint 2

Compare 50 cm with the focal length you found. Is the object at a special position?

Hint 3

For an object at 2F of a convex lens, where is the image and how big is it?

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.

  1. (in metres)

    ½ mark

  2. m cm. It is a convex (converging) lens.

    ½ mark

  3. Object distance is 50 cm , so the object is at . The image forms at (50 cm behind the lens) and is real and inverted, of the same size.

    ½ mark

  4. Magnification .

    ½ mark

  5. Ray diagram (described):

    • Draw a convex lens with the principal axis; mark , on the left and , on the right.
    • Place an upright object AB at .
    • Ray 1 from B runs parallel to the axis and refracts through .
    • Ray 2 from B passes undeviated through the optical centre O.
    • The rays meet at B′ below the axis at . Image A′B′ is inverted and equal in size to AB.
    • Show arrows on all rays.
    1 mark

Answer: f = +25 cm; image real and inverted, same size, m = −1 (formed at 2F₂)

Where the marks are

  • Uses (½ mark)
  • f = 0.25 m = 25 cm (½ mark)
  • Image real and inverted (½ mark)
  • Magnification = −1 (½ mark)
  • Correct ray diagram with object at 2F₁ and image at 2F₂; ½ deducted if ray arrows missing (1 mark)

Revise the chapter

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 31/4/1: 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.