PhysicsCBSE Class 12 · Board exam 2025, set 55/1/1 · 5 marks · Long answer

CBSE Class 12 Physics 2025: question 33(a)

Set in the CBSE Class 12 board exam of 2025, paper 55/1/1, section E, question 33(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(a) · 5 marks · Long answerWave Optics

(i) (1) What are coherent sources ? Why are they necessary for observing a sustained interference pattern ?
(2) Lights from two independent sources are not coherent. Explain.
(ii) Two slits 0.1 mm apart are arranged 1.20 m from a screen. Light of wavelength 600 nm from a distant source is incident on the slits.
(1) How far apart will adjacent bright interference fringes be on the screen ?
(2) Find the angular width (in degree) of the first bright fringe.

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

Think about what must stay constant between two waves for the bright and dark spots to stay in place.

Hint 2

Recall how light is emitted by the atoms of an ordinary lamp. Is there any link between the phases of two different lamps?

Hint 3

Use fringe width $β = λ D / d$ and angular width $= λ / d$ . Convert mm and nm to metres first.

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.

(i)(1) Two sources are coherent if they emit light of the same frequency (wavelength) and the phase difference between their waves stays zero or constant with time.
1 mark
A sustained interference pattern needs the phase difference at every point of the screen to stay constant. Only then do bright and dark fringes stay fixed in position. With incoherent sources the phase difference changes rapidly, the fringes shift many times a second, and the eye sees only uniform average intensity.
1 mark
(i)(2) In an ordinary source, light is emitted by millions of atoms independently and randomly, in short bursts of about $1 0^{- 8}$ s. The phase of light from one independent source changes randomly relative to the other, so their phase difference is not constant. Hence two independent sources can never be coherent.
1 mark
(ii)(1) The spacing of adjacent bright fringes is the fringe width:
$β = \frac{λ D}{d} = \frac{600 \times 1 0 ^{- 9} \times 1.20}{0.1 \times 1 0 ^{- 3}} = 7.2 \times 1 0^{- 3} m = 7.2 mm$
1 mark
(ii)(2) Angular width:
$θ = \frac{λ}{d} = \frac{600 \times 1 0 ^{- 9}}{0.1 \times 1 0 ^{- 3}} = 6 \times 1 0^{- 3} rad$
In degrees: $6 \times 1 0^{- 3} \times \frac{18 0 ^{\circ}}{π} \approx 0.3 4^{\circ}$
1 mark

Answer: (ii)(1) 7.2 mm; (2) $6 \times 1 0^{- 3}$ rad ≈ 0.34°

Where the marks are

Defines coherent sources as having the same frequency and a constant phase difference (1 mark)
Explains that a constant phase difference keeps the fringes fixed, which gives a sustained pattern (1 mark)
Explains that random emission from independent atoms gives a varying phase difference (1 mark)
Calculates fringe width $β = λ D / d = 7.2$ mm (1 mark)
Calculates angular width $λ / d = 6 \times 1 0^{- 3}$ rad ≈ 0.34° (1 mark; the radian answer alone earns full credit)

Revise the chapter

Chapter: Wave Optics (notes, formulas, where marks are lost and every past question)
Topic: Young's Double Slit Experiment

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 33(a)

Hints

Step-by-step solution

Revise the chapter

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