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Diffraction Grating

πŸ“Š advanced
$$d\sin\theta = m\lambda$$
Condition for constructive interference in diffraction grating.
Variables & Units
$d$
Grating spacing
Unit: $\text{m}$
$\theta$
Diffraction angle
Unit: $\text{rad}$ or $^\circ$
$m$
Order number
Unit: $\text{unitless}$
$\lambda$
Wavelength
Unit: $\text{m}$
Key Information
πŸ“ Derived From
Huygens' principle and interference
πŸ’‘ Example
Grating $d=1.67\times10^{-6}\,\text{m}$ (600 lines/mm), $\lambda=500\,\text{nm}$: $\sin\theta = (1\times500\times10^{-9})/(1.67\times10^{-6}) = 0.299$, $\theta \approx 17.4^\circ$ for $m=1$.
πŸ”§ Applications
Spectrometers, monochromators, wavelength measurement
⚠️ Constraints
Far-field (Fraunhofer) diffraction

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