Diffraction & the Diffraction Grating
Pass light through a single narrow gap and it doesn't travel straight through as a neat beam — it spreads out. That spreading, diffraction, becomes far more useful once thousands of slits are ruled side by side on a grating, turning a beam of light into a precise tool for measuring wavelength.
Diffraction through a single slit
Diffraction is the spreading out of a wave as it passes through a gap or around an obstacle. Every wave diffracts, but the effect is only obvious when the gap size is comparable to the wavelength — that's why sound (wavelengths of centimetres to metres) diffracts noticeably around doorways and corners, while light (a few hundred nanometres) needs a very narrow slit before its diffraction becomes visible.
Shine monochromatic light through a single narrow slit onto a distant screen and the pattern isn't a single sharp band matching the slit's shape. Instead there's a wide, bright central maximum directly opposite the slit, flanked by much dimmer secondary maxima, with dark minima in between. Intensity drops with each secondary maximum moving outward, and the central maximum is roughly twice as wide as any secondary maximum.
With white light instead of monochromatic light, the central maximum stays white (every wavelength reinforces at the centre, as with Young's central fringe), while the secondary maxima spread into smears of colour, since pattern width depends on wavelength and each colour diffracts by a slightly different amount.
What controls the width of the central maximum
Two things determine how widely the light spreads, and both can be reasoned through qualitatively.
A narrower slit produces a wider central maximum. In the extreme case, shrink the slit toward a single point source and the light has nowhere directional left to go — it spreads in almost every direction, filling the screen roughly evenly. Widen the slit and the light increasingly behaves like a beam the width of the slit, with diffraction becoming a smaller fraction of the pattern.
A longer wavelength produces a wider central maximum, for a similar reason: diffraction is more pronounced when the wavelength is large relative to the gap. A given slit width is a comparatively larger obstacle for shorter wavelengths, so short-wavelength light diffracts and spreads less; long-wavelength light diffracts and spreads more.
AQA doesn't require plotting or interpreting a full intensity-versus-angle graph for single-slit diffraction — only the qualitative relationship between the central maximum's width and the wavelength and slit width, described in words as above.
The diffraction grating
A diffraction grating is a plate ruled with a very large number of closely spaced parallel slits (thousands of lines per millimetre). Shining monochromatic light through a grating at normal incidence (perpendicular to the grating) produces sharp, narrow, well-separated bright spots at specific angles, rather than the broad hazy pattern from a single slit — light from every slit interferes constructively only at very particular angles, and destructively almost everywhere else.
Each bright spot is an order: the undeviated spot straight through is the zero order, and the spots on either side, at progressively larger angles, are the first order, second order, and so on.
Deriving the grating equation
The angles at which the bright orders appear follow from path difference, in much the same way as the bright fringes in Young's double-slit experiment.
Here $d$ is the grating spacing (often calculated from lines per metre, $N$, via $d = 1/N$), $\theta$ is the angle between the normal and a given bright order, and $n$ is the order number (0, 1, 2, …). Given a known grating spacing, measuring the angle to an order gives the wavelength directly — or a known wavelength can be used to find an unknown grating spacing.
AQA excludes the use of a spectrometer to measure diffraction angles — angles are found from simple geometry instead, typically by measuring distances on a screen a known distance from the grating and using trigonometry, in the same spirit as the double-slit fringe measurements.
As with Young's double-slit experiment, a laser is the typical light source used for grating experiments: already monochromatic and coherent, so the orders it produces are sharp, bright and easy to measure accurately.
Applications
Because the angle for a given order depends on wavelength, a grating illuminated with light containing several wavelengths — white light, or light from a gas discharge tube — spreads it into its component wavelengths at each order, similar to (but far more precisely than) a prism. This is the basis of spectroscopy: passing light from a star, a flame test, or a gas sample through a grating and measuring the angles of the resulting spectral lines reveals exactly which wavelengths, and so which elements, are present. Diffraction gratings are used throughout astronomy, chemistry and materials science to determine the precise composition of a light source.
Key takeaways
- Diffraction is the spreading of a wave through a gap or around an obstacle; it's most noticeable when the gap size is comparable to the wavelength.
- A single slit produces a wide central maximum flanked by much dimmer secondary maxima; a narrower slit or a longer wavelength both widen the central maximum.
- No intensity-vs-angle graph is required by AQA — only the qualitative width relationship.
- A diffraction grating (many closely spaced slits) produces sharp bright orders at specific angles under normal incidence, from constructive interference across all the slits simultaneously.
- The grating equation $d\sin\theta = n\lambda$ follows from path difference between adjacent slits equalling a whole number of wavelengths.
- AQA excludes the use of a spectrometer; angles are found by geometry from screen measurements instead.
- Diffraction gratings are used in spectroscopy to split light into its component wavelengths and identify the elements present in a source.