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Hold a concave mirror in your… (Class 10 Science 2023, Q39)

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ScienceCBSE Class 10 · Board exam 2023, set 31/1/1 · 4 marks · Case-based

CBSE Class 10 Science 2023: question 39

Set in the CBSE Class 10 board exam of 2023, paper 31/1/1, section E, question 39, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q39 · 4 marks · Case-basedCompetency-basedLight – Reflection and Refraction

Hold a concave mirror in your hand and direct its reflecting surface towards the sun. Direct the light reflected by the mirror on to a white card-board held close to the mirror. Move the card-board back and forth gradually until you find a bright, sharp spot of light on the board. This spot of light is the image of the sun on the sheet of paper; which is also termed as "Principal Focus" of the concave mirror.

  1. (a)

    List two applications of concave mirror.

    1 mark
  2. (b)

    If the distance between the mirror and the principal focus is 15 cm, find the radius of curvature of the mirror.

    1 mark
  3. (c)

    Draw a ray diagram to show the type of image formed when an object is placed between pole and focus of a concave mirror.

    2 marks

  4. OR

    (c)

    An object 10 cm in size is placed at 100 cm in front of a concave mirror. If its image is formed at the same point where the object is located, find :
    (i) focal length of the mirror, and
    (ii) magnification of the image formed with sign as per Cartesian sign convention.

    2 marks

Figure in the paper: Concave mirror with parallel rays from the left converging at the principal focus F on the principal axis; pole O on the mirror. Labels: Concave mirror, Principal axis, Principal Focus, F, O. See it in the official paper.

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

Hints

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

Hint 1

Think of devices that need a strong beam of light, or an enlarged face.

Hint 2

The radius of curvature and focal length of a mirror are related by a simple factor.

Hint 3

If the image forms at the object itself, the object must be at the centre of curvature. Use 1/v + 1/u = 1/f with Cartesian signs.

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. (a) Applications of a concave mirror: (1) in torches, searchlights and vehicle headlights, to get a strong parallel beam of light;

    ½ mark

  2. (2) as shaving mirrors / dentist's mirrors, to see an enlarged image (also used in solar furnaces).

    ½ mark

  3. (b) Focal length cm. For a spherical mirror,

    ½ mark

  4. cm

    ½ mark

  5. (c)(a) Ray diagram (described): draw a concave mirror with pole P, focus F and centre of curvature C on the principal axis. Place a small object AB between P and F. Ray 1: from A parallel to the principal axis; after reflection it passes through F. Ray 2: from A along the line joining C to A, striking the mirror normally; it reflects back along the same path. Mark arrows on all rays.

    1 mark

  6. The two reflected rays diverge. Extend them backwards with dotted lines; they meet behind the mirror at A′. Draw A′B′ perpendicular to the axis. The image is behind the mirror, virtual, erect and enlarged.

    1 mark

  7. (c)(b) [alternative choice, 2 marks if attempted instead of (c)(a)] (i) cm, cm. The image forms at the object's position, so cm. Mirror formula: (½ mark)

  8. , so cm. (Equivalently, the object is at C, so cm.) (½ mark)

  9. (ii) (½ mark) . The image is real, inverted and the same size (10 cm). (½ mark)

Answer: (a) e.g. torches/headlights/searchlights and shaving/dentist's mirrors; (b) R = 30 cm; (c)(a) image virtual, erect, enlarged, behind the mirror (ray diagram); (c)(b) (i) f = −50 cm, (ii) m = −1

Where the marks are

  • Any two correct applications (½ + ½ marks)
  • Uses R = 2f (½ mark)
  • R = 30 cm (½ mark)
  • Correct ray diagram with object between P and F, reflected rays extended to give a virtual, erect, enlarged image behind the mirror; ½ mark deducted if arrows are missing (2 marks)
  • OR (c): mirror formula with signs (½), f = −50 cm (½), m = −v/u (½), m = −1 (½) (2 marks)

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 31/1/1: 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.