# 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.

> IB DP Physics Higher Level (2023 syllabus) — C.3 Wave phenomena · Explain · 4 marks

> 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.

## Mark scheme (4 marks)

1. 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.
2. 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.
3. 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.
4. 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

- [diffraction grating](https://www.gradenine.co.uk/glossary/diffraction-grating)
- [slit separation](https://www.gradenine.co.uk/glossary/slit-separation)

## Related

- [Revision notes for IB DP Physics Higher Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
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