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

CBSE Class 12 Physics 2026: question 18(a)

Set in the CBSE Class 12 board exam of 2026, paper 55/1/1, section B, question 18(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q18(a) · 2 marks · Very short answerWave Optics

A beam of light consisting of two wavelengths 400 nm and 600 nm is used to illuminate a single slit of width 1 mm. Find the least distance of the point from the central maximum where the dark fringes due to both wavelengths coincide on the screen placed 1.5 m from the slit.

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

Hints

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

Hint 1

Dark fringes in single-slit diffraction occur where $a sin θ = nλ$ .

Hint 2

Find the smallest whole numbers $n_{1}$ and $n_{2}$ with $n_{1} (400) = n_{2} (600)$ .

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 single-slit diffraction the $n$ th minimum lies at $y_{n} = \frac{nλ D}{a}$ .
½ mark
For the minima to coincide: $n_{1} λ_{1} = n_{2} λ_{2} \Rightarrow n_{1} (400) = n_{2} (600) \Rightarrow \frac{n _{1}}{n _{2}} = \frac{3}{2}$ . The least distance corresponds to $n_{1} = 3$ , $n_{2} = 2$ .
½ mark
$y = \frac{3 \times 400 \times 1 0 ^{- 9} \times 1.5}{1 \times 1 0 ^{- 3}} = 1.8 \times 1 0^{- 3}$ m $= 1.8$ mm
1 mark

Answer: 1.8 mm from the central maximum

Where the marks are

Writes the position of a minimum, $y = nλ D / a$ (½ mark)
Coincidence condition $3 \times 400 = 2 \times 600$ (½ mark)
Least distance of 1.8 mm (1 mark)

Revise the chapter

Chapter: Wave Optics (notes, formulas, where marks are lost and every past question)
Topic: Single Slit Diffraction

Practise this chapterBoard-style questions from Wave Optics, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 55/1/1: every question, by section.

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CBSE Class 12 Physics 2026: question 18(a)

Hints

Step-by-step solution

Revise the chapter

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