PhysicsCBSE Class 12 · Board exam 2026, set 55/5/1 · 2 marks · Very short answer

CBSE Class 12 Physics 2026: question 20

Set in the CBSE Class 12 board exam of 2026, paper 55/5/1, section B, question 20, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q20 · 2 marks · Very short answerRay Optics and Optical Instruments

Two thin lenses of focal length $f_{1}$ and $f_{2}$ are placed in contact with each other coaxially. Prove that the focal length f of the combination is given by $f = \frac{f _{1} f _{2}}{f _{1} + f _{2}}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 55/5/1.

Hints

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

Hint 1

The image formed by the first lens acts as the object for the second lens.

Hint 2

Write the lens formula twice and add the equations — the intermediate image distance cancels.

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.

Let an object O be at distance u from the combination (lenses thin and in contact, so distances are measured from a common optical centre). Lens 1 alone forms image $I_{1}$ at $v_{1}$ :
$\frac{1}{v _{1}} - \frac{1}{u} = \frac{1}{f _{1}}$ ...(1)
½ mark
$I_{1}$ acts as a virtual object for lens 2, which forms the final image I at v:
$\frac{1}{v} - \frac{1}{v _{1}} = \frac{1}{f _{2}}$ ...(2)
½ mark
Adding (1) and (2): $\frac{1}{v} - \frac{1}{u} = \frac{1}{f _{1}} + \frac{1}{f _{2}}$
½ mark
If the combination is replaced by a single lens of focal length f giving the same image, $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ . Hence $\frac{1}{f} = \frac{1}{f _{1}} + \frac{1}{f _{2}} = \frac{f _{1} + f _{2}}{f _{1} f _{2}}$ , i.e. $f = \frac{f _{1} f _{2}}{f _{1} + f _{2}}$ .
(Ray diagram: object O, image $I_{1}$ by first lens beyond the lenses, final image I by second lens.)
½ mark

Answer: 1/f = 1/f₁ + 1/f₂ ⇒ f = f₁f₂/(f₁ + f₂)

Where the marks are

Lens formula for first lens giving intermediate image (½ mark)
Intermediate image used as object for second lens (½ mark)
Adding the two equations (½ mark)
Comparing with single equivalent lens to get the result (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 paper2026 board paper, set 55/5/1: every question, by section.

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CBSE Class 12 Physics 2026: question 20

Hints

Step-by-step solution

Revise the chapter

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