Single-Slit Diffraction
Adjust width, see central max. Builds on Young's Double-Slit.
You shine a laser through a single slit and observe the diffraction pattern on a distant screen. The central bright maximum is the biggest feature.
Compared to each side maximum, the central maximum is how wide?
Exactly twice as wide! The central maximum stretches from the first dark fringe on one side (m = -1) to the first dark fringe on the other (m = +1), spanning an angular width of 2λ/a. Each side maximum sits between consecutive dark fringes (e.g., m = 1 to m = 2), spanning only λ/a. The central max is twice the width of any side max. It’s also MUCH brighter — about 84% of all diffracted light falls in the central maximum.
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Observe the diffraction pattern intensity profile. Notice the central maximum is twice the width of the side maxima. Compare the brightness — the central peak is dramatically stronger. Adjust the slit width: narrower slit makes EVERYTHING wider (more diffraction).
I(θ) = I₀[sin(πa sinθ/λ) / (πa sinθ/λ)]²
The sinc-squared function [sin(x)/x]² is the ‘signature’ of single-slit diffraction. Its central peak is twice as wide as the side peaks, and the side peaks fall off rapidly. About 84% of all energy is in the central max.
A circular aperture produces a circular diffraction pattern (Airy disk). The central spot’s angular radius is 1.22λ/D. This sets the fundamental resolution limit of every telescope and camera lens.
Stopping down a camera lens too far (very small aperture) actually REDUCES image sharpness because of diffraction. There’s an optimal f-stop that balances aberrations (want small aperture) against diffraction (want large aperture).
A loudspeaker cone acts like a circular aperture for sound. Low frequencies (long λ) diffract widely, filling the room. High frequencies (short λ) beam forward. That’s why tweeters are small and woofers are large.
A radar dish’s angular resolution is limited by diffraction: θ ∼ λ/D. Larger dishes or shorter wavelengths give sharper images. This is why weather radar uses centimeter waves with large antennas.
“Squeeze light through a narrow slit and it fans out. The central bright band is twice as wide as the rest and holds most of the energy. Confinement breeds spreading — the wave’s way of rebelling against boundaries.”
Single-Slit Diffraction Lab
Explore single-slit diffraction with adjustable slit width and wavelength. Compare the intensity profile to the sinc-squared function. Measure the 2:1 width ratio of central to side maxima.
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Start with a moderate slit width and red light. Identify the central maximum and first side maxima. Measure their widths — verify the 2:1 ratio. Now narrow the slit: the entire pattern widens (counterintuitive!). Switch to blue light: the pattern narrows (shorter λ). Try making the slit very wide — the pattern tightens to a thin beam, approaching the geometric shadow. Toggle the intensity graph to see the sinc² envelope.
Single-slit diffraction produces a pattern where the central maximum is always exactly twice the width of each side maximum, and contains ~84% of the total light. Narrower slits produce wider patterns. This sinc² pattern is the building block for understanding all diffraction phenomena.