# Explain how the principle of superposition accounts for the formation of a dark fringe in a single-slit diffraction pattern at an angle where the slit width equals twice the wavelength of the incident light.

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

> Monochromatic light of wavelength λ is incident on a single slit of width b = 2λ. A dark fringe is observed on a distant screen at the first minimum of the diffraction pattern.

## Mark scheme (4 marks)

1. The slit can be divided into two equal halves, each of width λ, acting as a set of secondary sources (Huygens' sources).
2. For the first minimum, the path difference between the wavelet from the top of the slit and the wavelet from the midpoint of the slit is λ/2 (half a wavelength).
3. A path difference of λ/2 corresponds to a phase difference of π (180°), so each wavelet from the upper half is exactly out of phase with its corresponding wavelet from the lower half.
4. By the principle of superposition, the amplitudes of all paired wavelets cancel throughout the entire slit, giving zero resultant amplitude and hence a dark fringe at that angle.

## Key terms

- [principle of superposition](https://www.gradenine.co.uk/glossary/principle-of-superposition)
- [single-slit diffraction](https://www.gradenine.co.uk/glossary/single-slit-diffraction)

## 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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Source: [GradeNine](https://www.gradenine.co.uk/q/explain-how-the-principle-of-superposition-507156f0) · Published by Druglandscape Ltd.