Explain why increasing the number of slits in a diffraction grating, while keeping the slit separation constant, produces sharper and brighter principal maxima.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A diffraction grating consists of a large number of equally spaced slits. When monochromatic light passes through it, a pattern of sharp, bright maxima is observed at angles that satisfy the grating equation d sin θ = nλ.
Model answer (4 marks)
Each slit acts as a secondary source of light.
1. At a principal maximum the path difference between adjacent slits is an integer multiple of λ, so all N slits add in phase. The resultant amplitude is N times that of one slit, giving intensity ∝N² – the maxima become brighter.
2. Between maxima the path differences are not multiples of λ, so the waves from the many slits are out of phase. With more slits the phase differences cover a wider range, leading to more complete destructive interference.
3. The increased cancellation narrows the angular width of the bright peaks, making the principal maxima sharper.
4. The condition d sinθ=nλ depends only on d and λ, so the positions of the maxima do not change when N is increased.
1. At a principal maximum the path difference between adjacent slits is an integer multiple of λ, so all N slits add in phase. The resultant amplitude is N times that of one slit, giving intensity ∝N² – the maxima become brighter.
2. Between maxima the path differences are not multiples of λ, so the waves from the many slits are out of phase. With more slits the phase differences cover a wider range, leading to more complete destructive interference.
3. The increased cancellation narrows the angular width of the bright peaks, making the principal maxima sharper.
4. The condition d sinθ=nλ depends only on d and λ, so the positions of the maxima do not change when N is increased.
Examiner tips
- Use the word ‘constructive’ for the maxima and ‘destructive’ for the minima; mention intensity ∝N² for brightness.
- Explain that more slits give more phase differences between adjacent waves, leading to sharper peaks.
- Show that the grating equation is independent of N to justify unchanged positions.
Common mistakes
- Confusing the number of slits with slit width; the width does not affect the positions of the maxima.
- Failing to state that intensity increases as N² rather than just N.
- Assuming the angular width changes but not specifying that it narrows due to better cancellation.
Mark scheme (4 marks)
- Each additional slit contributes an additional wave/wavelet that can interfere constructively at a principal maximum, so the amplitude (and hence intensity) at those maxima increases.
- Between principal maxima, waves from the many slits have a range of path differences and therefore destructively interfere / cancel more completely.
- This more complete destructive interference in the regions between maxima means the bright maxima are confined to a narrower angular range, making them sharper / narrower.
- The positions of the principal maxima are unchanged because they depend only on the slit separation d and wavelength λ (via d sin θ = nλ), not on the number of slits.
Key terms in this question
diffraction grating · slit separation
Related
- All IB DP Physics Standard Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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