Snell's Law Refraction Calculator mechanism

Model scope

The core law is correct, but the specification is incomplete because it does not define angle units, angle reference direction, inverse-solving behavior, physical-domain validation, or total-internal-reflection handling. The verdict is NEEDS_REVIEW until those behaviors are specified.

• The relation n1 sin(theta1) = n2 sin(theta2) is the standard Snell's law formula for a planar interface, assuming isotropic, non-magnetic media and angles measured from the interface normal.
• The calculator must explicitly implement the inverse forms theta2 = asin((n1/n2) sin(theta1)) and theta1 = asin((n2/n1) sin(theta2)); the listed equation alone does not specify which angle is solved for.
• The valid inverse-sine domain must be enforced: if the argument magnitude exceeds 1, no real refracted angle exists because of total internal reflection.
• The physical branch should normally return angles from 0 to 90 degrees for ordinary refraction; this branch convention is not specified.

Units and conventions

• Refractive indices n1 and n2 are dimensionless.
• Angles in the test vectors are in degrees, and inverse-trigonometric results are converted back to degrees. The specification does not state whether the implementation expects degrees or radians.
• Angles are measured from the interface normal, not from the interface surface.
• The media are assumed homogeneous, isotropic, and non-magnetic; refractive index values are wavelength- and condition-dependent.
• For ordinary transparent media, n1 and n2 are assumed positive and nonzero.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "mode": "solve_theta2",
    "n1": 1,
    "n2": 1.5,
    "theta1_deg": 0
  },
  "expected_outputs": {
    "theta2_deg": 0
  },
  "working": "sin(theta2) = (n1/n2) sin(theta1) = (1.0/1.5) sin(0 degrees) = (2/3)(0) = 0. Therefore theta2 = asin(0) = 0 degrees."
}

Failure boundary

• If n2 is zero, the inverse formula divides by zero.
• If n1 or n2 is negative, the physical interpretation requires handling complex or signed refractive indices; this is not specified.
• For light going from a higher-index medium to a lower-index medium, an input above the critical angle produces an inverse-sine argument greater than 1 and must be reported as total internal reflection rather than NaN or a fabricated angle.
• Passing degree values directly to JavaScript Math.sin or Math.asin, which use radians, causes incorrect results; explicit conversion is required.
• The interface-normal convention is not stated, so complementary angle results are possible if users measure from the surface.
• A refractive-index table requires wavelength, temperature, pressure, and material-state assumptions; a generic air/water/glass/diamond table can be misleading without those qualifiers.

Other records

Sources and evidence

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

• VERIFIED_LEDGER.json
• evidence-tranche5/tranche5-results.json