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.
Viewing angle, angular distance and angle 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.
In any particular example of a ray of light passing through a raindrop, the angle of deviation and theangle 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.