Diffraction Grating⚠ unverified
Physics / Optics · Compute the diffraction angle of a grating for a given order
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| lambda_ | λ_ | m | 1.0 | Wavelength of the light |
| d | d | m | 1.0 | Grating period (slit spacing) |
| m | m | — | 1.0 | Diffraction order (dimensionless integer) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | mλ | — | Diffraction angle, in degrees. Returns NaN when the order is evanescent (``abs(sin(theta)) > 1``) |
The science & history
Understanding the Parameters
- $d$ — lines per metre $= 1/d$.
- $m$ — $m=0$ specular; $\pm 1,\pm 2,\ldots$ spectral orders.
- $m\lambda/d$ — must be ≤ 1 for a real angle.
Derivation (Approaching a Proof)
Path difference between adjacent slits/grooves is $d\sin\theta$. Constructive interference when that equals $m\lambda$ (normal incidence).
History
Diffraction gratings (Rittenhouse, Fraunhofer, Rowland) are the core of spectroscopy.
Related Concepts: Youngs Double Slit, Diffraction Single Slit, Rayleigh Criterion
Notes: Registry calculator diffraction-grating (unverified). Ambiguous I/O — equation vs
inputs/outputs need Track B alignment.