Explain why increasing the number of slits in a diffraction grating, while keeping the slit separation constant, causes the principal maxima to become narrower and brighter.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A diffraction grating is used to analyse the spectrum of light from a distant star. The grating has N slits, each separated by a distance d.
Model answer (4 marks)
1. The principal maxima occur at angles given by d\sin\theta=n\lambda, which are independent of the number of slits, so their positions do not change.
2. With more slits, the waves from each slit add constructively at the principal angles, giving a larger resultant amplitude; intensity ∝ amplitude², so the maxima become brighter.
3. Between two adjacent principal maxima there are (N−1) secondary maxima and (N−1) minima; increasing N spreads the destructive interference over a wider angular range around each principal maximum.
4. Because the total incident energy is conserved, the energy that is now concentrated into the narrower, brighter principal maxima is taken from the minima and reduced secondary maxima, keeping the overall energy balance.
2. With more slits, the waves from each slit add constructively at the principal angles, giving a larger resultant amplitude; intensity ∝ amplitude², so the maxima become brighter.
3. Between two adjacent principal maxima there are (N−1) secondary maxima and (N−1) minima; increasing N spreads the destructive interference over a wider angular range around each principal maximum.
4. Because the total incident energy is conserved, the energy that is now concentrated into the narrower, brighter principal maxima is taken from the minima and reduced secondary maxima, keeping the overall energy balance.
Examiner tips
- Use the formula d sinθ = nλ to state that angles are unchanged; mention constructive interference for brightness; note the increase in secondary maxima/minima count; reference energy conservation to explain narrowing.
- Show the relationship between amplitude and intensity (I∝A²) to justify brightness.
- Explain that more slits give a higher-order interference pattern with sharper peaks.
Common mistakes
- Claiming the angles of maxima change with N; confusing width with intensity.
- Forgetting that intensity is proportional to the square of the amplitude, not the amplitude itself.
- Ignoring the role of energy conservation and the spread of minima/secondary maxima.
Mark scheme (4 marks)
- The principal maxima occur at the same angles (given by d sin θ = nλ) regardless of the number of slits, so their angular positions do not change.
- The principal maxima are brighter because more slits contribute more waves that interfere constructively, increasing the amplitude (and hence the intensity, which is proportional to amplitude squared) at the maxima.
- Between adjacent principal maxima there are (N − 1) secondary maxima and N − 1 minima (or equivalently N − 2 secondary maxima); as N increases, the destructive interference conditions spread across a wider angular range around each principal maximum.
- Since total energy/power incident on the grating is conserved, the energy concentrated into narrower, brighter principal maxima is balanced by the minima and reduced secondary maxima between them.
Key terms in this question
diffraction grating · slit separation
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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