Source: https://guthlabs.ai/docs/instruments/double-slit-single-slit-diffraction-calculator/

instrument / verified-clean

# Double-Slit / Single-Slit Diffraction Calculator

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/double-slit-single-slit-diffraction-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/double-slit-single-slit-diffraction-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/double-slit-single-slit-diffraction-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/double-slit-single-slit-diffraction-calculator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo

**Tranche**: tranche-6

**Evidence ID**: t6-101

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The position formulas are recognizable Fraunhofer/paraxial formulas after correcting the double-slit condition, but the supplied double-slit expression is malformed and the claimed intensity-pattern output lacks an algorithm. Because the instrument claims both fringe positions and intensity plotting, these omissions make the specification FAIL rather than PASS.

### Formula and scope findings

- The double-slit condition is written as "y sinθ≈mλ", which is not the standard condition. The standard condition is d sinθ=mλ, with screen position y=L tanθ; under the small-angle approximation, y≈mλL/d and fringe spacing Δy≈λL/d.

- The single-slit condition a sinθ=mλ correctly gives minima only for nonzero integer orders m=±1,±2,...; m=0 is the central maximum, not a minimum.

- The claimed intensity pattern has no intensity formula. A complete Fraunhofer model needs, for example, normalized double-slit interference I/I0=cos²(πd sinθ/λ) and normalized single-slit diffraction I/I0=[sin(πa sinθ/λ)/(πa sinθ/λ)]², plus assumptions about slit illumination, relative phase, slit widths, and polarization.

- The fringe-spacing formula Δy=λL/d is a paraxial approximation and is not valid without a far-field/small-angle constraint. Exact fringe positions require θ=arcsin(mλ/d) and y=L tanθ.

- The Fraunhofer label is honest but incomplete: the specification should state that L must be sufficiently large compared with slit dimensions, commonly expressed through a small Fresnel number or an explicit far-field validity condition.

### Unit assumptions

- Use SI units internally: λ, slit width a, and slit separation d in metres; L and screen coordinate y in metres.

- The wavelength λ is the vacuum wavelength unless a medium refractive index is explicitly supplied; in a medium, use λ=λ0/n.

- The positional formulas use the paraxial approximation sinθ≈tanθ≈y/L.

- For the intensity test vectors, the inferred normalized ideal formulas are double slit I/I0=cos²(πdy/(λL)) and single slit I/I0=[sin(πay/(λL))/(πay/(λL))]². These formulas are not actually present in the supplied specification.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The specification exposes several unhandled edge hazards: d=0 produces undefined division, orders with |mλ/d|>1 produce no real diffraction angle, and m=0 in the single-slit formula is the central maximum rather than a minimum. Signed-order reporting is also convention-dependent. The supplied specification does not provide enough parameters or an intensity formula to compute a quantitative intensity pattern.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "mode": "double_slit",
    "slit_separation_d": "0.50 mm",
    "wavelength_lambda": "600 nm",
    "screen_distance_L": "2.00 m",
    "sampled_screen_positions_y": [
      "-1.20 mm",
      "0 mm",
      "1.20 mm"
    ],
    "normalized_intensity_model": "cos²(π d y/(λ L))",
    "position_model": "y_m≈mλL/d"
  },
  "expected_outputs": {
    "fringe_spacing": "2.400 mm",
    "fringe_positions": {
      "m=-1": "-2.400 mm",
      "m=0": "0 mm",
      "m=1": "2.400 mm"
    },
    "sampled_normalized_intensity": {
      "y=-1.20 mm": "0",
      "y=0 mm": "1",
      "y=1.20 mm": "0"
    },
    "curve_features": {
      "bright_maxima": "y=m(2.400 mm), m integer",
      "dark_minima": "y=(m+1/2)(2.400 mm), m integer"
    }
  },
  "working": "Convert units: λ=600 nm=0.000000600 m; d=0.50 mm=0.000500 m; L=2.00 m. Fringe spacing: Δy=λL/d=(0.000000600×2.00)/0.000500=0.000001200/0.000500=0.002400 m=2.400 mm. Positions: y_m≈mΔy, so y_{-1}=-2.400 mm, y_0=0, y_1=2.400 mm. For y=-1.20 mm, πy/Δy=π(-1.20/2.40)=-π/2, so I/I0=cos²(-π/2)=0. For y=0, I/I0=cos²(0)=1. For y=1.20 mm, πy/Δy=π/2, so I/I0=cos²(π/2)=0. Bright maxima occur when πy/Δy=mπ, giving y=mΔy. Dark minima occur when πy/Δy=(m+1/2)π, giving y=(m+1/2)Δy."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`