Angular distance - Light, Colour, Vision

When discussing rainbows, angular distance is the angle between the rainbow axis and the direction in which an observer must look to see a specific colour within the arcs of a rainbow.

Angular distance, viewing angle and angle of deflection all produce the same value measured in degrees.
Angular distance is a measurement on a ray-tracing diagram that represents the Sun, an observer and a rainbow in side elevation.
Think of angular distance as an angle between the centre of a rainbow and its coloured arcs with red at 42.4⁰ and violet at 40.7⁰.
Angular distances for different colours are constants determined by the laws of refraction and reflection.
The elevation of the Sun, the location of the observer and exactly where rain is falling are all variables that determine where a rainbow will appear to an observer.
The coloured arcs of a rainbow form the circumference of circles (discs or cones) and share a common centre.
The angular distance to any specific colour is the same whatever point is selected on the circumference.
The angular distance for any observed colour in a primary bow is between 42.4⁰ and violet at 40.7⁰.
The angular distance for any observed colour in a secondary bow is between 53.4⁰ and 50.4⁰ from its centre.
The angular distance can be calculated for any specific colour visible within a rainbow.
Considered from an observer’s viewpoint, it is clear that all incident rays seen by an observer run parallel with each other as they approach a raindrop.
Most of the observable incident rays that strike a raindrop follow paths that place them outside the range of possible viewing angles. The unobserved rays are all deflected towards the centre of a rainbow.

About viewing angles, angular distance and angles of deflection

The term viewing angle refers to the number of degrees through which an observer must move their eyes or turn their head to see a specific colour within the arcs of a rainbow.
The term angular distance refers to the same measurement when shown in side elevation on a diagram.
The angle of deflection measures the degree to which a ray striking a raindrop is bent back on itself in the process of refraction and reflection towards an observer.
The term rainbow ray refers to the path taken by the deflected ray that produces the most intense colour experience for any particular wavelength of light passing through a raindrop.
The term angle of deviation measures the degree to which the path of a light ray is bent back by a raindrop in the course of refraction and reflection towards an observer.
- In any particular example of a ray of light passing through a raindrop, the angle of deviation and the angle of deflection are directly related to one another and together add up to 180⁰.
- The angle of deviation is always equal to 180⁰ minus the angle of deflection. So clearly the angle of deflection is always equal to 180⁰ minus the angle of deviation.
- In any particular example, the angle of deflection is always the same as the viewing angle because the incident rays of light that form a rainbow are all approaching on a trajectory running parallel with the rainbow axis.