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How do waves spread out through gaps and around obstacles, and how does a diffraction grating split light into spectra?

Diffraction of waves at a single slit, the appearance of the single-slit pattern with white light and monochromatic light, the diffraction grating, the grating equation, and its applications in spectra.

A focused answer to AQA A-Level Physics 3.3.2.3, covering diffraction at a single slit, the single-slit pattern with monochromatic and white light, the diffraction grating, the grating equation and applications in producing spectra.

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  1. What this dot point is asking
  2. Diffraction at a single slit
  3. Single slit with white light
  4. The diffraction grating
  5. Try this

What this dot point is asking

AQA specification point 3.3.2.3 wants you to describe diffraction at a single slit, explain the single-slit intensity pattern for monochromatic and white light, describe the diffraction grating, use the grating equation, and explain how a grating produces spectra.

Diffraction at a single slit

For monochromatic light through a single slit, the pattern is a wide, bright central maximum with dimmer maxima of decreasing brightness on each side, separated by dark fringes. The central maximum is twice the width of the others and contains most of the light energy. Narrowing the slit widens the central maximum, because narrower gaps cause more diffraction.

Single slit with white light

With white light the central maximum is white (all wavelengths overlap at the centre, where every colour has zero path difference), while the outer maxima are spread into spectra, with violet (shorter wavelength) closest to the centre and red furthest out, because longer wavelengths diffract more.

The diffraction grating

Because the angle depends on wavelength, a grating spreads different colours to different angles, producing a spectrum at each order. This makes gratings the basis of spectrometers used to measure wavelengths and to analyse the light from stars, where they can resolve very close spectral lines. A grating gives much sharper and more widely separated maxima than a prism, and the separation can be calculated precisely from the grating equation, which is why gratings have largely replaced prisms in research spectrometers. The maximum observable order is found by setting sin⁡θ=1\sin\theta = 1, giving nmax⁡=dλn_{\max} = \dfrac{d}{\lambda} rounded down to a whole number.

Try this

Q1. State when diffraction through a gap is most noticeable. [1 mark]

  • Cue. When the gap width is about the same as the wavelength.

Q2. Explain why a diffraction grating gives sharper maxima than a double slit. [2 marks]

  • Cue. Many slits mean constructive interference only occurs at very precise angles, so the maxima are narrow and bright.

Q3. State which colour appears closest to the centre in a single-slit white-light pattern. [1 mark]

  • Cue. Violet (it has the shortest wavelength and diffracts least).

Exam-style practice questions

Practice questions written in the style of AQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

AQA 20194 marksA diffraction grating with 300300 lines per millimetre is illuminated normally with monochromatic light of wavelength 590 nm590 \text{ nm}. Calculate the angle of the second-order maximum.
Show worked answer →

Find the slit spacing: d=1×10−3300=3.33×10−6 md = \dfrac{1 \times 10^{-3}}{300} = 3.33 \times 10^{-6} \text{ m}.

Apply the grating equation dsin⁡θ=nλd\sin\theta = n\lambda with n=2n = 2: sin⁡θ=nλd=2×590×10−93.33×10−6=0.354\sin\theta = \dfrac{n\lambda}{d} = \dfrac{2 \times 590 \times 10^{-9}}{3.33 \times 10^{-6}} = 0.354.

So θ=sin⁡−1(0.354)=20.7∘\theta = \sin^{-1}(0.354) = 20.7^{\circ}.

Markers reward converting lines per mm to a slit spacing in metres, correct substitution with n=2n = 2, and the inverse sine for the angle.

AQA 20213 marksDescribe and explain the appearance of the diffraction pattern produced when white light passes through a single narrow slit.
Show worked answer →

The central maximum is white, because all wavelengths overlap and recombine at the centre where the path difference is zero for every colour.

The outer maxima are spread into spectra (coloured fringes), because longer wavelengths diffract more. Violet (shortest wavelength) appears closest to the centre and red (longest) furthest out in each outer fringe.

The central maximum is also the widest and brightest, twice the width of the subsidiary maxima.

Markers reward the white central maximum, the outer maxima dispersed into colours, and violet inside red because longer wavelengths diffract more.

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