PhysicsCBSE Class 12 · Sample paper, session 2023-24 · 2 marks · Very short answer

CBSE Class 12 Physics sample paper 2023-24: question 21(b)

From the official CBSE sample question paper for 2023-24, section B, question 21(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(b) · 2 marks · Very short answerRay Optics and Optical Instruments

In an astronomical telescope in normal adjustment a straight black line of length L is drawn on the objective lens. The eyepiece forms a real image of this line whose length is $l$ . What is the angular magnification of the telescope?

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

The line on the objective is an object for the eyepiece at distance $f_{o} + f_{e}$ .

Hint 2

Find the eyepiece's linear magnification and compare it with $f_{o} / f_{e}$ .

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.

In normal adjustment the separation of objective and eyepiece is $f_{o} + f_{e}$ . The line on the objective acts as an object for the eyepiece: $u = - (f_{o} + f_{e})$ , $f = f_{e}$ .
$\frac{1}{v} - \frac{1}{- ( f _{o} + f _{e} )} = \frac{1}{f _{e}} \Rightarrow \frac{1}{v} = \frac{1}{f _{e}} - \frac{1}{f _{o} + f _{e}} = \frac{f _{o}}{f _{e} ( f _{o} + f _{e} )} \Rightarrow v = \frac{f _{e} ( f _{o} + f _{e} )}{f _{o}}$
1 mark
Linear magnification by the eyepiece: $\frac{v}{u} = \frac{f _{e}}{f _{o}} = \frac{image size}{object size} = \frac{l}{L}$
½ mark
Angular magnification of the telescope: $M = \frac{f _{o}}{f _{e}} = \frac{L}{l}$
½ mark

Answer: $M = f_{o} / f_{e} = L / l$

Where the marks are

Applies lens formula for eyepiece with $u = - (f_{o} + f_{e})$ and finds $v$ (1 mark)
Finds linear magnification $f_{e} / f_{o} = l / L$ (½ mark)
Concludes $M = f_{o} / f_{e} = L / l$ (½ 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 21(b)

Hints

Step-by-step solution

Revise the chapter

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