PhysicsCBSE Class 12 · Board exam 2025, set 55/7/1 · 2 marks · Very short answer

CBSE Class 12 Physics 2025: question 18(b)

Set in the CBSE Class 12 board exam of 2025, paper 55/7/1, section B, question 18(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q18(b) · 2 marks · Very short answerRay Optics and Optical Instruments

A convex lens of focal length 10 cm, a concave lens of focal length 15 cm and a third lens of unknown focal length are placed coaxially in contact. If the focal length of the combination is +12 cm, find the nature and focal length of the third lens, if all lenses are thin. Will the answer change if the lenses were thick ?

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

Powers of thin lenses in contact simply add.

Hint 2

A concave lens has a negative focal length; solve for 1/f₃ and look at its sign.

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.

For thin lenses in contact: $\frac{1}{F} = \frac{1}{f _{1}} + \frac{1}{f _{2}} + \frac{1}{f _{3}}$ , with $f_{1} = + 10$ cm, $f_{2} = - 15$ cm and $F = + 12$ cm.
½ mark
Substituting: $\frac{1}{f _{3}} = \frac{1}{12} - \frac{1}{10} + \frac{1}{15} = \frac{5 - 6 + 4}{60} = \frac{3}{60}$ .
½ mark
$f_{3} = + 20$ cm. The third lens is convex (converging).
½ mark
Yes, the answer would change. The formula $1/ F = \sum 1/ f_{i}$ holds only for thin lenses in contact; for thick lenses, the separations between their optical centres cannot be neglected.
½ mark

Answer: Third lens is convex with f = +20 cm; yes, the result would change for thick lenses.

Where the marks are

Writes the combination formula for thin lenses in contact (½ mark)
Correct substitution with proper signs (½ mark)
f₃ = +20 cm, convex lens (½ mark)
States that the answer changes for thick lenses, with reason (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 paper2025 board paper, set 55/7/1: every question, by section.

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CBSE Class 12 Physics 2025: question 18(b)

Hints

Step-by-step solution

Revise the chapter

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