Diffraction Single Slit⚠ unverified
Physics / Optics · Compute the single-slit diffraction intensity factor
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| lambda_ | λ_ | m | 1.0 | Wavelength of the light |
| a | a | m | 1.0 | Slit width |
| theta | θ | — | 1.0 | Observation angle from the central axis, in degrees |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | I/I0 | — | Normalized intensity factor (dimensionless), in the range [0, 1]. Returns 1.0 at the central maximum where ``beta == 0`` |
The science & history
Understanding the Parameters
- $a$, $\lambda$, $\theta$ — first minima when $a\sin\theta = m\lambda$ ($m=\pm 1,\pm 2,\ldots$).
- $I/I_0$ — 1 on axis ($\beta\to 0$ limit); falls in a sinc² pattern.
Derivation (Approaching a Proof)
Fraunhofer diffraction: integrate phasors across the slit. The amplitude is proportional to $\mathrm{sinc}(\beta)$ with $\beta = \pi a\sin\theta/\lambda$; intensity is the square.
History
Single-slit diffraction is the classic wave-optics demonstration and the envelope of multi-slit patterns.
Related Concepts: Diffraction Grating, Youngs Double Slit, Rayleigh Criterion
Notes: Registry calculator diffraction-single-slit (unverified). Confirm $\beta$ construction
in code; $\theta$ in radians.