A highly polished surface such as a mirror reflects most of the light falling on it. In our daily life we use two types of mirrors — plane and spherical. The reflecting surface of a spherical mirrors may be curved inwards or outwards. In concave mirrors, reflection takes place from the inner surface, while in convex mirrors reflection takes place from the outer surface. (a) Define the principal axis of a concave mirror. (b) A ray of light is incident on a concave mirror, parallel to its principal axis. If this ray after reflection from the mirror passes through the principal axis from a point at a distance of 10 cm from the pole of the mirror, find the radius of curvature of the mirror. (c) (i) An object is placed at a distance of 10 cm from the pole of a convex mirror of focal length 15 cm. Find the position of the image. (c) (ii) A mirror forms a virtual, erect and diminished image of an object. Identify the type of this mirror. Draw a ray diagram to show the image formation in this case.

ScienceCBSE Class 10 · Board exam 2024, set 31/5/1 · 4 marks · Case-based

CBSE Class 10 Science 2024: question 39

Set in the CBSE Class 10 board exam of 2024, paper 31/5/1, 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

A highly polished surface such as a mirror reflects most of the light falling on it. In our daily life we use two types of mirrors — plane and spherical. The reflecting surface of a spherical mirrors may be curved inwards or outwards. In concave mirrors, reflection takes place from the inner surface, while in convex mirrors reflection takes place from the outer surface.

(a)
Define the principal axis of a concave mirror.
1 mark
(b)
A ray of light is incident on a concave mirror, parallel to its principal axis. If this ray after reflection from the mirror passes through the principal axis from a point at a distance of 10 cm from the pole of the mirror, find the radius of curvature of the mirror.
1 mark
(c)
(i) An object is placed at a distance of 10 cm from the pole of a convex mirror of focal length 15 cm. Find the position of the image.
2 marks
OR
(c)
(ii) A mirror forms a virtual, erect and diminished image of an object. Identify the type of this mirror. Draw a ray diagram to show the image formation in this case.
2 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 31/5/1.

Hints

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

Hint 1

Where does a ray parallel to the principal axis go after reflection from a concave mirror?

Hint 2

Remember R = 2f, and for a convex mirror f is positive while u is negative.

Hint 3

Which mirror gives a small, upright image for every object position? Use one ray parallel to the axis and one towards C.

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) The principal axis of a concave mirror is the imaginary straight line passing through its pole (P) and its centre of curvature (C).
1 mark
(b) A ray parallel to the principal axis passes through the principal focus after reflection, so $f = 10 cm$ .
Radius of curvature: $R = 2 f = 2 \times 10 = 20 cm$ .
1 mark
(c)(i) For a convex mirror, using the sign convention: $u = - 10 cm$ , $f = + 15 cm$ .
Mirror formula: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
½ mark
$\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{15} - \frac{1}{- 10} = \frac{1}{15} + \frac{1}{10}$
½ mark
$\frac{1}{v} = \frac{2 + 3}{30} = \frac{1}{6}$ , so $v = + 6 cm$ .
The image is formed 6 cm behind the mirror. It is virtual and erect.
1 mark
(c)(ii) A mirror that always forms a virtual, erect and diminished image is a convex mirror (diverging mirror).
½ mark
Ray diagram (in words): Draw a convex mirror with pole P on the principal axis, and F and C behind the mirror. Place object AB upright in front of the mirror.
- Ray 1 from A runs parallel to the principal axis. After reflection it diverges, appearing to come from F; extend it backwards as a dotted line.
- Ray 2 from A is directed towards C. It reflects straight back along the same path; extend it as a dotted line towards C.
- The dotted lines meet at A' behind the mirror, between P and F. Drop A'B' perpendicular to the axis.
A'B' is virtual, erect and diminished. Arrows must show the direction of the rays.
1½ marks

Answer: (a) Line through the pole and centre of curvature; (b) R = 20 cm; (c)(i) v = +6 cm (6 cm behind the mirror, virtual and erect); (c)(ii) Convex mirror, with the ray diagram showing the image between P and F behind the mirror

Where the marks are

Defines the principal axis as the line through the pole and centre of curvature (1 mark)
Takes f = 10 cm and finds R = 2f = 20 cm (1 mark)
Writes the mirror formula and substitutes with correct signs (½ + ½ mark)
Gets v = +6 cm, i.e. behind the mirror (1 mark)
Identifies the mirror as convex (½ mark)
Draws a correct ray diagram with arrows; ½ mark is deducted if ray directions are not shown (1½ marks)

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 31/5/1: every question, by section.

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CBSE Class 10 Science 2024: question 39

Hints

Step-by-step solution

Revise the chapter

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