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(i) State Huygens'… (Class 12 Physics 2024, Q33b)

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PhysicsCBSE Class 12 · Board exam 2024, set 55/1/1 · 5 marks · Long answer

CBSE Class 12 Physics 2024: question 33(b)

Set in the CBSE Class 12 board exam of 2024, paper 55/1/1, section E, question 33(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(b) · 5 marks · Long answerWave Optics

(i) State Huygens' principle. A plane wave is incident at an angle i on a reflecting surface. Construct the corresponding reflected wavefront. Using this diagram, prove that the angle of reflection is equal to the angle of incidence.
(ii) What are the coherent sources of light? Can two independent sodium lamps act like coherent sources? Explain.
(iii) A beam of light consisting of a known wavelength 520 nm and an unknown wavelength , used in Young's double slit experiment produces two interference patterns such that the fourth bright fringe of unknown wavelength coincides with the fifth bright fringe of known wavelength. Find the value of .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 55/1/1.

Hints

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

Hint 1

In the time the far end of the wavefront reaches the surface, the wavelet from the near end grows to the same radius.

Hint 2

Coherence needs a constant phase difference. Think about how atoms in a lamp emit light.

Hint 3

Equate the positions of the 4th bright fringe of λ and the 5th bright fringe of 520 nm.

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.

  1. (i) Huygens' principle:

    • Every point on a wavefront acts as a source of secondary wavelets, which spread out in all directions with the speed of the wave.
    • The common tangent (forward envelope) to these wavelets gives the new position of the wavefront at a later time.
    ½ mark

  2. Construction (described in words): A plane wavefront AB meets the reflecting surface MN at A, making an angle with it.

    • Point B of the wavefront travels a distance to reach the surface at C in time .
    • In the same time, the secondary wavelet from A spreads into a hemisphere of radius above the surface.
    • The tangent CE from C to this hemisphere is the reflected wavefront. It makes angle with the surface.
    ½ mark

  3. Proof: Compare right triangles ABC and AEC:

    • [wavefront ⟂ ray]
    • hypotenuse AC is common

    So the triangles are congruent (RHS). Hence , that is, .

    The angle of reflection equals the angle of incidence.

    1 mark

  4. (ii) Coherent sources are sources that emit light of the same frequency with a phase difference that stays constant in time.

    ½ mark

  5. No. Two independent sodium lamps cannot act as coherent sources. In each lamp, light comes from millions of atoms emitting randomly and independently, in short bursts of about s. So the phase difference between the two lamps changes rapidly and randomly.

    As a result, any interference pattern shifts so fast that only uniform average illumination is seen.

    1 mark

  6. (iii) The position of the th bright fringe is .

    Condition for coincidence:

    ½ mark

  7. Solving:

    1 mark

Answer: (i) i = r proved via congruent triangles; (ii) constant phase difference; No – independent lamps have randomly varying phase; (iii) λ = 650 nm

Where the marks are

  • Statement of Huygens' principle (½ mark)
  • Construction of the reflected wavefront (½ mark)
  • Proof of i = r using congruent triangles (1 mark)
  • Definition of coherent sources (½ mark)
  • No, with the reason that phase varies randomly between independent lamps (1 mark)
  • Sets up 4λD/d = 5(520)D/d (½ mark)
  • λ = 650 nm (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Wave Optics, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 55/1/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.