Diffraction Gratings
White light → spectrum. Builds on Single-Slit Diffraction.
You compare two setups: a standard double slit (2 slits) and a diffraction grating with 10,000 slits, both with the same slit spacing d. Both are illuminated with the same monochromatic laser.
What makes the grating’s peaks so much sharper than the double slit’s?
More slits = sharper peaks! With N slits, the angular width of each peak is proportional to 1/N. A double slit (N=2) has broad peaks. A grating with N = 10,000 has peaks 5,000 times narrower! The reason: at the exact Bragg angle, all N waves add in phase. Move slightly off that angle, and waves from different slits start canceling. More slits = more cancellation for off-angle light = sharper peaks. The peak intensity also grows as N².
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Start with 2 slits and observe the broad fringe pattern. Increase to 5, 10, 50, then 1000 slits. Watch the peaks sharpen dramatically while staying at the same angular positions. The minor maxima between peaks also become more numerous (N-2 of them).
d sinθ = mλ R = mN
Resolution depends on the TOTAL number of lines illuminated times the order. More lines or higher order = better resolution. That’s why research gratings are as large as possible and why higher-order spectra are used for precision work.
Astronomers use diffraction gratings to decompose starlight into precise spectra. From spectral lines, they determine a star’s composition, temperature, velocity, and magnetic field — all from the grating’s ability to resolve closely spaced wavelengths.
The data tracks on optical discs act as reflection gratings. CDs have ~1.6 μm spacing, DVDs ~0.74 μm, Blu-ray ~0.32 μm. That’s why you see rainbow reflections — and why each format reads with a different laser wavelength.
Lab spectrometers use gratings with thousands of lines per millimeter to identify chemicals. Each element has a unique spectral fingerprint. Forensics, environmental testing, and drug analysis all rely on grating spectroscopy.
Modern gratings are made by recording laser interference patterns on photoresist (holographic gratings). They have fewer defects than ruled gratings and can be blazed (tilted grooves) to concentrate light into a preferred order.
“A double slit whispers about wavelength. A grating with ten thousand slits screams it with precision. More slits, sharper peaks, clearer spectra.”
Diffraction Grating Lab
Explore how the number of slits transforms broad interference bumps into razor-sharp spectral lines. Adjust N, d, and wavelength. Resolve closely spaced wavelengths. See white-light spectra emerge.
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Start with N=2 slits and monochromatic red light. Note the broad peaks. Increase N to 5, 20, 100, 1000 — watch peaks sharpen dramatically. Now use two wavelengths close together (e.g., sodium D lines at 589.0 and 589.6 nm). With N=2, they’re unresolved. Increase N until two distinct peaks appear — that’s the resolving power in action! Try white light to see the full rainbow spectrum at each diffraction order.
The grating equation d sinθ = mλ locates the peaks. The number of slits N controls their sharpness (width ∝ 1/N) and the resolving power R = mN. More slits = sharper peaks = better spectral resolution. This is the foundation of all modern spectroscopy.