PhysicsCBSE Class 12 · Sample paper, session 2024-25 · 2 marks · Very short answer

CBSE Class 12 Physics sample paper 2024-25: question 18(II)

From the official CBSE sample question paper for 2024-25, section B, question 18(II), for 2 marks. Try it first; the hints and our step-by-step solution are below.

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

In Young's double-slit experiment using monochromatic light of wavelength λ, the intensities of two sources are I. What is the intensity of light at a point where path difference between wavefronts is λ/4?

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

Recall the formula for the resultant intensity of two coherent waves with a phase difference φ.

Hint 2

Phase difference = (2π/λ) × path difference.

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.

Resultant intensity of two interfering waves: $I_{R} = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ$
½ mark
With $I_{1} = I_{2} = I$ : $I_{R} = 2 I (1 + cos ϕ) = 4 I cos^{2} \frac{ϕ}{2}$
½ mark
Phase difference for a path difference of $λ /4$ : $ϕ = \frac{2 π}{λ} \times \frac{λ}{4} = \frac{π}{2}$
½ mark
$I_{R} = 4 I cos^{2} \frac{π}{4} = 4 I \times \frac{1}{2} = 2 I$
½ mark

Answer: $I_{R} = 2 I$

Where the marks are

Writes the resultant-intensity formula (½ mark)
Simplifies it to $4 I cos^{2} (ϕ /2)$ (½ mark)
Converts the path difference to phase difference $π /2$ (½ mark)
Gets the result $2 I$ (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 paperSample paper 2024-25: every question, by section.

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CBSE Class 12 Physics sample paper 2024-25: question 18(II)

Hints

Step-by-step solution

Revise the chapter

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