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Diffraction Grating

N slits → sharp intensity peaks when d·sin(θ) = m·λ. Resolving power R = mN

Optics Wave Physics Interferometry Spectroscopy

Light:

Slits N 6 Spacing d 2.0 µm Slit width a 0.5 µm

Wavelength λ 550 nm

N = 6 slits θ₁ = —° Orders visible: — Resolving power R = — λ/Δλ min = —

🌈 Fraunhofer Diffraction Grating

A diffraction grating with N slits of spacing d and width a produces a far-field intensity pattern (Fraunhofer limit):

I(θ) = I₀ · sinc²(β) · [sin(Nδ/2)/sin(δ/2)]²

where β = πa·sin(θ)/λ (single-slit envelope) and δ = 2πd·sin(θ)/λ (inter-slit phase).

Principal maxima: d·sin(θ) = m·λ (m = 0, ±1, ±2, …)
Resolving power: R = mN — the grating can resolve λ/Δλ = mN apart
Angular dispersion: dθ/dλ = m/(d·cos θ)
Missing orders: when a/d = integer, the single-slit zero cancels a grating maximum

White light mode shows all visible wavelengths (380–750 nm) simultaneously, revealing the rainbow spectrum in each order — the principle behind spectrographs.