Explain why a single narrow slit produces a diffraction pattern with a bright central maximum flanked by alternating dark and bright fringes of decreasing intensity.

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).

Monochromatic light of wavelength 550 nm is directed at a single narrow slit. A screen placed far from the slit shows a diffraction pattern consisting of a bright central maximum and several secondary maxima of diminishing brightness on either side.

Model answer (4 marks)

1. Each point on the slit acts as a source of secondary wavelets (Huygens’ principle). 2. The wavelets interfere beyond the slit; at the centre of the screen the path difference between all wavelets is zero, giving constructive interference and a bright central maximum. 3. Dark fringes occur when the path difference between wavelets from opposite edges of the slit is a half‑wavelength (or odd multiple), producing complete destructive interference. 4. Secondary maxima are less bright because only a portion of the wavelets interfere constructively; the constructive fraction decreases for higher‑order fringes, so the intensity falls off.

Examiner tips

  • Use Huygens’ principle and path‑difference arguments; mention constructive vs destructive interference; explain why central maximum is brightest; note intensity decreases with order.

Common mistakes

  • Confusing the condition for minima (half‑wavelength) with maxima; forgetting that the central maximum is due to zero path difference; not explaining why higher maxima are dimmer.

Mark scheme (4 marks)

  1. Each point on the wavefront within the slit acts as a source of secondary wavelets (Huygens' principle), and these wavelets superpose / interfere beyond the slit.
  2. The central maximum is bright because wavelets from across the entire slit arrive at the centre of the screen with zero path difference, so they interfere constructively.
  3. Dark fringes (minima) occur at angles where wavelets from different parts of the slit can be paired so that each pair has a path difference of half a wavelength, resulting in complete destructive interference.
  4. Secondary maxima are less bright than the central maximum because only a fraction of the slit's wavelets contribute constructively (the remaining wavelets cancel), and the fraction contributing constructively decreases for higher-order maxima.

Key terms in this question

diffraction · central maximum

Related

More Wave phenomena questions

▶ Try answering this question with AI marking (free) →