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

CBSE Class 12 Physics 2025: question 18(b)

Set in the CBSE Class 12 board exam of 2025, paper 55/1/1, 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 answerWave Optics

In a Young's double-slit experiment, two light waves, each of intensity $I_{o}$ , interfere at a point, having a path difference $\frac{λ}{8}$ on the screen. Find the intensity at this point.

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

Hints

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

Hint 1

First change the path difference into a phase difference using $ϕ = \frac{2 π}{λ} Δ x$ .

Hint 2

Then use $I = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ$ with equal intensities.

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.

Phase difference $ϕ = \frac{2 π}{λ} \times Δ x = \frac{2 π}{λ} \times \frac{λ}{8} = \frac{π}{4}$ .
½ mark
Resultant intensity: $I = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ$ , with $I_{1} = I_{2} = I_{o}$ .
½ mark
$I = I_{o} + I_{o} + 2 I_{o} cos \frac{π}{4} = 2 I_{o} + 2 I_{o} \times \frac{1}{2}$ .
½ mark
$I = (2 + 2) I_{o} \approx 3.414 I_{o}$ . (Equivalently, $I = 4 I_{o} cos^{2} \frac{π}{8}$ .)
½ mark

Answer: I = (2 + √2) I₀ ≈ 3.41 I₀

Where the marks are

Converts the path difference to phase difference $π /4$ (½ mark)
Writes the resultant intensity formula (½ mark)
Substitutes correctly (½ mark)
Gets $I = (2 + 2) I_{o} \approx 3.414 I_{o}$ (½ mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Wave Optics, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 55/1/1: 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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