PhysicsCBSE Class 12 · Board exam 2025, set 55/7/1 · 5 marks · Long answer

CBSE Class 12 Physics 2025: question 33(a)

Set in the CBSE Class 12 board exam of 2025, paper 55/7/1, section E, question 33(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(a) · 5 marks · Long answerRay Optics and Optical Instruments

(i) Explain with the help of a labelled ray diagram the formation of final image by an astronomical telescope at infinity. Write the expression for its magnifying power.
(ii) The total magnification produced by a compound microscope is 20. The magnification produced by the eyepiece is 5. When the microscope is focussed on a certain object, the distance between the objective and eyepiece is observed to be 14 cm. Calculate the focal lengths of the objective and the eyepiece. (Given that the least distance of distinct vision = 25 cm)

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 55/7/1.

Hints

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

Hint 1

Total magnification of a compound microscope is $m_{o} \times m_{e}$ ; with the final image at $D$ , $m_{e} = 1 + D / f_{e}$ .

Hint 2

Use the lens formula on the eyepiece to locate its object. The objective–eyepiece distance is $v_{o} + ∣ u_{e} ∣$ .

Hint 3

Use $∣ m_{o} ∣ = v_{o} /∣ u_{o} ∣$ to get $u_{o}$ , then apply the lens formula to the objective.

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) Ray diagram (normal adjustment):
- Draw the objective lens $O$ (large aperture, long focal length $f_{o}$ ) and the eyepiece $E$ (short focal length $f_{e}$ ) on a common principal axis.
- Parallel rays from a distant object enter the objective inclined at angle $α$ to the axis.
- After refraction they meet at the focal plane of the objective and form a real, inverted, diminished image $A^{'} B^{'}$ at distance $f_{o}$ behind $O$ .
- $A^{'} B^{'}$ lies at the first focus of the eyepiece, so the rays leave $E$ parallel, at angle $β$ to the axis.
- Arrows are shown on all rays.
1½ marks
Working: Light from the distant object forms a real, inverted image $A^{'} B^{'}$ at the focus of the objective. This image acts as the object for the eyepiece. Since it lies at the focus of the eyepiece, the eyepiece forms the final, highly magnified, inverted image at infinity.
½ mark
Magnifying power: $m = \frac{β}{α} = - \frac{f _{o}}{f _{e}}$ , with magnitude $\frac{f _{o}}{f _{e}}$ . Tube length $L = f_{o} + f_{e}$ .
1 mark
(ii) Total magnification $m = m_{o} m_{e}$ , so $20 = m_{o} \times 5$ , giving $∣ m_{o} ∣ = 4$ .
Final image at $D$ : $m_{e} = 1 + \frac{D}{f _{e}}$ , so $5 = 1 + \frac{25}{f _{e}}$ and $f_{e} = \frac{25}{4} = 6.25$ cm.
Object distance for the eyepiece (with $v_{e} = - 25$ cm): $\frac{1}{v _{e}} - \frac{1}{u _{e}} = \frac{1}{f _{e}}$ , so $- \frac{1}{25} - \frac{1}{u _{e}} = \frac{4}{25}$ , which gives $u_{e} = - 5$ cm.
1 mark
Separation $L = v_{o} + ∣ u_{e} ∣$ , so $14 = v_{o} + 5$ and $v_{o} = 9$ cm.
$∣ m_{o} ∣ = \frac{v _{o}}{∣ u _{o} ∣} = 4$ , so $∣ u_{o} ∣ = \frac{9}{4}$ cm, i.e. $u_{o} = - \frac{9}{4}$ cm.
Lens formula: $\frac{1}{f _{o}} = \frac{1}{v _{o}} - \frac{1}{u _{o}} = \frac{1}{9} + \frac{4}{9} = \frac{5}{9}$ .
So $f_{o} = \frac{9}{5} = 1.8$ cm.
1 mark

Answer: (i) $m = f_{o} / f_{e}$ (in magnitude) for final image at infinity; (ii) $f_{o} = 1.8$ cm, $f_{e} = 6.25$ cm

Where the marks are

Labelled ray diagram of astronomical telescope in normal adjustment, with arrows on rays (1½ marks)
Explains image formation at the focus of the objective and final image at infinity (½ mark)
Magnifying power $m = f_{o} / f_{e}$ (1 mark)
Finds $m_{o} = 4$ , $f_{e} = 25/4$ cm and $u_{e} = - 5$ cm (1 mark)
Finds $v_{o} = 9$ cm, $u_{o} = - 9/4$ cm and $f_{o} = 9/5$ cm (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 paper2025 board paper, set 55/7/1: every question, by section.

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CBSE Class 12 Physics 2025: question 33(a)

Hints

Step-by-step solution

Revise the chapter

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