Answer the following. (i) Draw a ray diagram to show the path of the reflected ray in each of the following cases : A ray of light incident on a convex mirror (1) parallel to its principal axis, and (2) is directed towards its principal focus. (ii) A 1.5 cm tall candle flame is placed perpendicular to the principal axis of a concave mirror of focal length 12 cm. If the distance of the flame from the pole of the mirror is 18 cm, use mirror formula to determine the position and size of the image formed.

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

CBSE Class 10 Science 2024: question 36(b)

Set in the CBSE Class 10 board exam of 2024, paper 31/3/1, section D, question 36(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q36(b) · 5 marks · Long answerLight – Reflection and Refraction

Answer the following.

(i)
Draw a ray diagram to show the path of the reflected ray in each of the following cases : A ray of light incident on a convex mirror (1) parallel to its principal axis, and (2) is directed towards its principal focus.
0 marks
(ii)
A 1.5 cm tall candle flame is placed perpendicular to the principal axis of a concave mirror of focal length 12 cm. If the distance of the flame from the pole of the mirror is 18 cm, use mirror formula to determine the position and size of the 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

For a convex mirror, F lies behind the mirror. Rays parallel to the axis appear to come from F after reflection, and the reverse is also true.

Hint 2

Use $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ with both u and f negative for a concave mirror.

Hint 3

For mirrors, $m = - \frac{v}{u}$ . A negative h' means the image is inverted.

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 convex mirror.
- Draw a convex mirror, its principal axis, and F and C behind the mirror.
- Draw a ray, with an arrow, parallel to the principal axis striking the mirror.
- The reflected ray goes back outwards, away from the axis.
- Extend it behind the mirror with a dotted line; the extension passes through the principal focus F.
- So the reflected ray appears to diverge from F.
1 mark
(i)(2) Ray diagram: ray directed towards the principal focus of a convex mirror.
- Draw a ray, with an arrow, aimed towards F behind the mirror. Show the part behind the mirror as a dotted line.
- After reflection the ray travels back 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): $h = + 1.5$ cm, $u = - 18$ cm, focal length of concave mirror $f = - 12$ cm. Unknowns: $v = ?$ , $h^{'} = ?$
½ mark
(ii) Mirror formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
½ mark
(ii) Substituting:
$\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{- 12} - \frac{1}{- 18} = \frac{- 3 + 2}{36} = - \frac{1}{36}$
$∴ v = - 36 cm$
The image is formed 36 cm in front of the mirror, on the same side as the object. It is a real image.
1 mark
(ii) Magnification: $m = \frac{h ^{'}}{h} = - \frac{v}{u}$
½ mark
(ii) Size of image:
$\frac{h ^{'}}{1.5} = - \frac{( - 36 )}{( - 18 )} = - 2$
$h^{'} = - 2 \times 1.5 = - 3.0 cm$
The image is 3 cm tall. It is real, inverted and twice the size of the flame.
½ mark

Answer: (i) (1) reflected ray appears to diverge from F; (2) reflected ray goes parallel to the principal axis. (ii) v = −36 cm (36 cm in front of the mirror, real); h' = −3.0 cm (3 cm tall, inverted, magnified)

Where the marks are

Correct ray diagram for a ray parallel to the axis of a convex mirror, with arrows (1 mark)
Correct ray diagram for a ray directed towards F, with arrows (1 mark)
Writes the given values with correct signs (½ mark)
Writes the mirror formula (½ mark)
Calculates v = −36 cm (1 mark)
Writes $m = h^{'} / h = - v / u$ (½ mark)
Calculates h' = −3.0 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(b)

Hints

Step-by-step solution

Revise the chapter

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