Rainbow Primary 42 Degree Angle
Compute stationary single internal-reflection spherical-drop rainbow ray under caller wavelength-specific refractive index; not a fixed 42 degree lookup or visible bow forecast.
Description
The primary rainbow arises from refraction and one internal reflection in a spherical water drop.
The primary rainbow arises from refraction and one internal reflection in a spherical water drop. Its angular radius depends on refractive index, including wavelength dependence.1
Compute stationary single internal-reflection spherical-drop rainbow ray under caller wavelength-specific refractive index; not a fixed 42 degree lookup or visible bow forecast.
When to use Rainbow Primary 42 Degree Angle
Use this tool to compute stationary single internal-reflection spherical-drop rainbow ray under caller wavelength-specific refractive index; not a fixed 42 degree lookup or visible bow forecast.
Prepare the observed sounding, cloud records or forecast verification data. Check pressure and height coordinates, wind conventions and the stated units.
How to use Rainbow Primary 42 Degree Angle and understand its results
- Prepare the observed sounding, cloud records or forecast verification data. Check pressure and height coordinates, wind conventions and the stated units.
- Enter relativeWaterRefractiveIndex using the field table and calculation rules, then run the tool.
- Read stationaryIncidenceDegrees, stationaryDeviationDegrees, rainbowRadiusFromAntisolarDegrees. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| relativeWaterRefractiveIndex | Relative water refractive index | number | Required |
Supply a relative water refractive index strictly between 1 and 2. Compute the stationary incidence and refraction angles, then report incidence, deviation and |D−π| in degrees about the antisolar direction.
i = acos(sqrt((n²−1)/3)); r = asin(sin(i)/n); D = π + 2i − 4r Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| stationaryIncidenceDegrees | Stationary incidence degrees | number |
| stationaryDeviationDegrees | Stationary deviation degrees | number |
| rainbowRadiusFromAntisolarDegrees | Rainbow radius from antisolar degrees | number |
{
"input": {
"relativeWaterRefractiveIndex": 1.3333333333333333
},
"output": {
"stationaryIncidenceDegrees": 59.39110234029069,
"stationaryDeviationDegrees": 137.97034113430232,
"rainbowRadiusFromAntisolarDegrees": 42.02965886569768
}
}Limitations and assumptions
A nominal 42-degree angle is not embedded. Drop shape, brightness, dispersion across wavelengths and visibility are outside this single-ray model.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Double Rainbow Secondary 51 Degree: Compute stationary double internal-reflection spherical-drop rainbow ray under caller wavelength-specific refractive index; not a fixed 51 degree lookup or visible bow forecast. For a complementary task, use Halo 22 Degree Ice Crystal Checker: Compare observed angular radius to ideal 60-degree hexagonal ice-prism minimum deviation under caller index/tolerance; angular agreement does not prove ice crystal habit, visible halo or sun-viewing safety.
References
-
Rainbow Primary 42 Degree Angle — tool.io
Similar or alternative tools
- Double Rainbow Secondary 51 Degree
Compute stationary double internal-reflection spherical-drop rainbow ray under caller wavelength-specific refractive index; not a fixed 51 degree lookup or visible bow forecast.
- Halo 22 Degree Ice Crystal Checker
Compare observed angular radius to ideal 60-degree hexagonal ice-prism minimum deviation under caller index/tolerance; angular agreement does not prove ice crystal habit, visible halo or sun-viewing safety.