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.

Description

The secondary rainbow involves two internal reflections in a spherical water drop.

The secondary rainbow involves two internal reflections in a spherical water drop. Its stationary deviation differs from the primary bow and varies with wavelength-specific refractive index.^[1]

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.

When to use Double Rainbow Secondary 51 Degree

Use this tool to 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.

Prepare the observed sounding, cloud records or forecast verification data. Check pressure and height coordinates, wind conventions and the stated units.

How to use Double Rainbow Secondary 51 Degree 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 relative refractive index in (1,3). Compute the double-reflection stationary ray and return incidence, deviation and absolute deviation from π in degrees around the antisolar direction.

i = acos(sqrt((n²−1)/8)); r = asin(sin(i)/n); D = 2π + 2i − 6r

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

json

{
  "input": {
    "relativeWaterRefractiveIndex": 1.3333333333333333
  },
  "output": {
    "stationaryIncidenceDegrees": 71.83197124269303,
    "stationaryDeviationDegrees": 230.97809352567572,
    "rainbowRadiusFromAntisolarDegrees": 50.97809352567572
  }
}

Limitations and assumptions

A fixed 51-degree angle and visible-bow prediction are not provided. Drop deformation and brightness are excluded.

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 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. 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

Double Rainbow Secondary 51 Degree — tool.io

Similar or alternative tools

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.
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.