Explain why, in a single-slit diffraction experiment, the central maximum is broader and more intense than the secondary maxima.

IB DP Physics Higher 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).

A monochromatic light source illuminates a narrow single slit. A diffraction pattern is observed on a distant screen.

Model answer (4 marks)

The central maximum is produced where the path difference between wavelets from all parts of the slit is zero (or less than one wavelength), so all the wavelets arrive in phase and interfere constructively. It extends from the first minimum on one side to the first minimum on the other, giving it an angular width twice that of any secondary maximum. Secondary maxima occur where the path difference is such that the wavelets from the slit only partially cancel; only a fraction of the slit contributes to constructive interference (roughly one‑third, one‑fifth, etc.). Consequently, the central maximum contains a far larger number of in‑phase wavelets and therefore has a much greater intensity than the secondary maxima.

Examiner tips

  • Show the constructive interference condition for the centre; mention the first minima to give the width. Explain that secondary maxima arise from incomplete cancellation. Link the number of contributing wavelets to intensity.
  • common_mistakes
  • :
  • Confusing the width of the central maximum with that of a secondary maximum. Saying the central maximum is broader because of diffraction without citing the first minima. Claiming secondary maxima are as intense as the centre without explaining the reduced constructive contribution.

Mark scheme (4 marks)

  1. The central maximum forms where path difference between wavelets from across the slit is zero (or less than one wavelength), so all wavelets arrive in phase and interfere constructively.
  2. The central maximum spans from the first minimum on one side to the first minimum on the other, giving it an angular width twice that of any secondary maximum.
  3. Secondary maxima form where wavelets from the slit only partially cancel, leaving a fraction of the wavelets contributing to constructive interference (approximately one-third, one-fifth, etc. of the slit contributes).
  4. Therefore the intensity of the central maximum is much greater than that of secondary maxima because a far greater number of wavelets contribute to its resultant amplitude.

Key terms in this question

single-slit diffraction

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