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Diffraction and the single slit

Waves spread out when they pass an edge or a gap. It happens at every gap, at every size, but the spreading only becomes dramatic when the gap shrinks towards the size of the wavelength.

Year 12AQA 3.3.2.2

Builds on Progressive waves.

IN THIS TOPIC

  • Describe diffraction at a gap and state when the spreading is greatest.
  • Sketch the single-slit intensity pattern and describe how slit width and wavelength change it.
  • Describe the single-slit pattern produced by white light.

WHAT YOU PROBABLY THINK

Waves only diffract when the gap is smaller than the wavelength.

Spreading at a gap

Pass a wave through a gap in a barrier and the wavefronts beyond it curve at the edges. The wave bends into the region that straight-line travel would leave empty. This spreading is diffraction, and it happens at every gap and every edge; the only question is how much.

Wavefronts at a wide gap and at a gap about one wavelength acrosssmall spreadlarge spreadgap ≈ 3λgap ≈ λ
FIG. 1The same wavelength meeting two gaps. Much wider than λ, the wave passes almost straight through, curling only at the edges. At a gap near λ, it spreads into semicircles.

The controlling comparison is gap size against wavelength. A gap much larger than λ lets the wave through nearly unchanged. As the gap narrows towards the wavelength, the spreading grows, and it is greatest when the gap is about the same size as the wavelength. This is why you hear a conversation through an open door without seeing the speakers: sound wavelengths are around a metre, comparable to the doorway, while light wavelengths are ten million times smaller, so the light passes straight through.

The single-slit pattern

Shine monochromatic light, light of a single wavelength, through a slit not much wider than the wavelength, and the screen beyond does something richer than a simple smear. It shows a bright central maximum, then darkness, then much fainter fringes alternating with dark minima on each side.

Single-slit intensity: a wide central maximum with weak, narrower maxima either sidepositioncentral maximumfirst minimum2ww
FIG. 2The single-slit intensity pattern. The central maximum is twice the width of the faint maxima beside it, which carry only a few per cent of its intensity.

Two features identify the pattern in an exam. The central maximum is twice the width of every other maximum, and it is far brighter than any of them. AQA asks for no equation here; what you need is the shape and how it responds when something changes.

Make the slit narrower and the whole pattern spreads wider, though dimmer, because less light gets through. Use a longer wavelength and the pattern also spreads wider, since the gap is now closer to λ. Red light therefore makes a wider pattern than blue through the same slit.

White light

White light is every visible wavelength at once, and each wavelength builds its own pattern with its own width. All of them share the middle of the screen, so the centre stays white. Away from the centre the patterns separate: each side fringe becomes a little spectrum, with violet on its inner edge, closest to the centre, and red on its outer edge, because the longer wavelengths spread more. Further out still, the overlapping spectra wash out.

THE EXAM BIT

  • “Explain when diffraction is most noticeable” wants the comparison stated: when the gap is about the same size as the wavelength. An answer that says “small gap” without mentioning λ is incomplete.
  • The single-slit shape carries the marks: central maximum twice the width of the side maxima and much brighter, with dark minima between.
  • Narrower slit: wider, dimmer pattern. Longer wavelength: wider pattern. Say which quantity you are changing and which way the pattern responds.
  • For white light, name the two ends: central white maximum, side fringes as spectra with violet nearest the centre and red furthest.
  • No single-slit formula is on the AQA paper. If you find yourself hunting the data sheet for one, the question is qualitative.

CHECK YOURSELF

A red laser and a blue laser shine in turn through the same narrow slit. Which produces the wider central maximum, and why?

Show a hint

Which colour has the longer wavelength?

Show the answer

The red laser. Red light has a longer wavelength than blue, so the slit width is closer to λ for red light, and the diffraction is stronger.

Stronger diffraction means the light spreads through a larger angle beyond the slit, so every feature of the pattern, including the central maximum, is wider for red than for blue.

Every gap diffracts.

A gap near λ diffracts most.

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