Explain why, in a double-slit interference experiment using monochromatic light, the bright fringes are equally spaced but their intensities are not all equal.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
In a double-slit interference experiment, a screen is placed at a large distance from two narrow slits separated by a distance d. The slits are illuminated by a monochromatic plane wave.
Model answer (4 marks)
1. Constructive interference occurs when the path difference between the two slits is an integer multiple of the wavelength, nλ. 2. The path difference varies linearly with the position on the screen, so the angles (and therefore the positions) where constructive interference occurs are equally spaced. 3. Each slit also diffracts light, producing a single‑slit diffraction envelope that modulates the intensity of the interference fringes. 4. The envelope is strongest at the centre and falls off towards the edges; consequently, bright fringes near the centre are intense, while those further out are weaker or even absent if they coincide with a diffraction minimum.
Examiner tips
- Use the path‑difference condition to justify equal spacing; mention linear variation with angle. Explain the diffraction envelope as a multiplicative factor on the interference intensity. Show that intensity varies with distance from the centre. Mention missing fringes at diffraction minima.
Common mistakes
- Confusing the interference pattern with the diffraction envelope; writing that all fringes are equally intense. Failing to state that the envelope is a multiplicative factor. Using vague terms like "spread out" instead of "equally spaced".
Mark scheme (4 marks)
- Equal fringe spacing arises because constructive interference occurs wherever the path difference between the two sources equals a whole number of wavelengths (nλ), and these positions are equally spaced on the screen.
- Each slit acts as a source of diffracted waves, so the intensity at any point on the screen is also modulated by the single-slit diffraction envelope.
- Bright fringes near the centre of the diffraction envelope (near the central diffraction maximum) have higher intensity, while those further from the centre have lower intensity.
- Some bright fringes from the interference pattern coincide with minima of the single-slit diffraction envelope and are therefore missing (have zero or near-zero intensity).
Related
- All IB DP Physics Higher Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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