Explain why the central maximum in a single-slit diffraction pattern becomes wider when the width of the slit is decreased.

IB DP Physics Standard Level (2023 syllabus) — C.3 Wave phenomena · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Model answer (4 marks)

Diffraction occurs when waves pass through the slit, causing the waves to spread out beyond the slit.
The angle at which the first minimum occurs is given by sin θ≈λ/b, where b is the slit width.
When the slit width b decreases, the ratio λ/b increases, so the angle to the first minimum increases.
The central maximum spans the region between the two first minima, so a larger angle to each first minimum means the central maximum is wider.

Examiner tips

  • Use the formula sin θ≈λ/b to link slit width to diffraction angle.
  • Explain that the central maximum is bounded by the first minima on either side.
  • Show the relationship between a larger θ and a wider angular spread.
  • Keep the answer concise and use the exact terminology from the mark scheme.

Common mistakes

  • Confusing the width of the central maximum with the slit width itself.
  • Using the wrong equation (e.g., sin θ=λ/2b).
  • Failing to mention that the central maximum is between the first minima.

Mark scheme (4 marks)

  1. Diffraction occurs as waves pass through the slit, causing the waves to spread out beyond the slit
  2. The angle at which the first minimum occurs is given by sin θ ≈ λ/b, where b is the slit width
  3. As slit width b decreases, the ratio λ/b increases, so the angle to the first minimum increases
  4. The central maximum spans the region between the two first minima, so a larger angle to each first minimum means the central maximum is wider

Key terms in this question

diffraction · central maximum

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