PhysicsCBSE Class 12 · Sample paper, session 2023-24 · 4 marks · Case-based

CBSE Class 12 Physics sample paper 2023-24: question 30

From the official CBSE sample question paper for 2023-24, section D, question 30, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q30 · 4 marks · Case-basedCompetency-basedRay Optics and Optical Instruments

Read the following paragraph and answer the questions that follow.
Types of Lenses and their combination
A convex or converging lens is thicker at the centre than at the edges. It converges a beam of light on refraction through it. It has a real focus. Convex lens is of three types: Double convex lens, Plano convex lens and Concavo-convex lens.
Concave lens is thinner at the centre than at the edges. It diverges a beam of light on refraction through it. It has a virtual focus. Concave lenses are of three types: Double concave lens, Plano concave lens and Convexo-concave lens.
When two thin lenses of focal lengths $f_{1}$ and $f_{2}$ are placed in contact with each other along their common principal axis, then the two lens system is regarded as a single lens of focal length f and
$\frac{1}{f} = \frac{1}{f _{1}} + \frac{1}{f _{2}}$
If several thin lenses of focal length $f_{1}, f_{2}, ... f_{n}$ are placed in contact, then the effective focal length of the combination is given by
$\frac{1}{f} = \frac{1}{f _{1}} + \frac{1}{f _{2}} + ..... + \frac{1}{f _{n}}$
and in terms of power, we can write
P = P1 + P2 + .... + Pn
The value of focal length and power of a lens must be used with proper sign consideration.

i.
Two thin lenses are kept coaxially in contact with each other and the focal length of the combination is 80 cm. If the focal length of one lens is 20 cm, the focal length of the other would be
1. (A)-26.7cm
2. (B)60cm
3. (C)80cm
4. (D)30cm
1 mark
ii.
A spherical air bubble is embedded in a piece of glass. For a ray of light passing through the bubble, it behaves like a
1. (A)converging lens
2. (B)diverging lens
3. (C)mirror
4. (D)thin plane sheet of glass
1 mark
iii.
Lens generally used in magnifying glass is
1. (A)single concave lens
2. (B)single convex lens
3. (C)combination of convex lens of lower power and concave lens of lower focal length
4. (D)Planoconcave lens
1 mark
iv.
The magnification of an image by a convex lens is positive only when the object is placed
1. (A)at its focus F
2. (B)between F and 2F
3. (C)at 2F
4. (D)between F and optical centre
1 mark
OR
iv.
A convex lens of 20 cm focal length forms a real image which is three times magnified. The distance of the object from the lens is
1. (A)13.33 cm
2. (B)14 cm
3. (C)26.66 cm
4. (D)25 cm
1 mark

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Use $1/ f = 1/ f_{1} + 1/ f_{2}$ with signs.

Hint 2

An air bubble in glass is a convex lens of a rarer medium; does it converge or diverge light?

Hint 3

For a real image, magnification is negative; put $v = 3∣ u ∣$ into the lens formula.

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) $\frac{1}{f _{2}} = \frac{1}{f} - \frac{1}{f _{1}} = \frac{1}{80} - \frac{1}{20} = - \frac{3}{80} \Rightarrow f_{2} = - 26.7$ cm. Option (a).
1 mark
(ii) The air bubble is a biconvex shape of a rarer medium (air) inside a denser medium (glass), so it spreads light out and acts as a diverging lens. Option (b).
1 mark
(iii) A single convex lens with the object placed within its focal length gives an erect, magnified, virtual image, so it is used as a magnifying glass. Option (b).
1 mark
(iv)(a) Positive magnification means an erect, virtual image, which a convex lens forms only when the object is between F and the optical centre. Option (d).
1 mark
(iv)(b) Real image, $m = - 3 \Rightarrow v = - 3 u$ . With $u = - x$ , $v = 3 x$ : $\frac{1}{3 x} + \frac{1}{x} = \frac{1}{20} \Rightarrow \frac{4}{3 x} = \frac{1}{20} \Rightarrow x = 26.66$ cm. Option (c).

Answer: (i) (a) −26.7 cm; (ii) (b); (iii) (b); (iv) (d) OR (c) 26.66 cm

Where the marks are

(i) −26.7 cm, option (a) (1 mark)
(ii) diverging lens, option (b) (1 mark)
(iii) single convex lens, option (b) (1 mark)
(iv) between F and optical centre, option (d); OR 26.66 cm, option (c) (1 mark)

Revise the chapter

Chapter: Ray Optics and Optical Instruments (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Ray Optics and Optical Instruments, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2023-24: every question, by section.

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CBSE Class 12 Physics sample paper 2023-24: question 30

Hints

Step-by-step solution

Revise the chapter

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