34: Diffraction
- Page ID
- 166356
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In the last chapter, two slits gave us a row of interference fringes. It is natural to push on the idea: if two slits make a pattern, what does one slit do? What about five slits, or a million? The answer is that a single slit makes a pattern of its own (a bright central band flanked by weaker fringes) and that adding more slits does not blur this into a wash of light but sharpens it into a row of needle-thin lines. The same physics, scaled from one opening to millions, runs from the blur at the edge of a shadow all the way to the instrument that first revealed the spacing of atoms in a crystal.
This spreading of waves as they pass an aperture or an edge is diffraction, and it is not a separate phenomenon from interference: it is interference, among the infinitely many Huygens wavelets that fan out from across a single opening. Diffraction sets a hard limit on the sharpness of every image ever formed: it is why a telescope, however perfect its mirror, cannot resolve two stars too close together, and why your own eye has a finite acuity. It also gives us the most powerful tools we have for taking light apart by wavelength and for reading the atomic architecture of matter. We will work from the single slit outward, to its intensity pattern, to circular apertures and the resolution of instruments, to the double slit seen afresh, to the diffraction grating, and finally to X-rays scattering from the planes of a crystal.
Learning Objectives
- Locate the minima of a single-slit diffraction pattern and find the width of the central maximum.
- Compute the intensity at any angle in single-slit diffraction.
- Apply the resolution limit of a circular aperture and Rayleigh’s criterion.
- Describe how single-slit diffraction modulates the double-slit interference pattern.
- Use the grating equation and understand why many slits give sharp, bright lines.
- Apply Bragg’s law to the diffraction of X-rays by crystals.
We will return to the opening question (one slit, many slits) as the through-line of the chapter.