The angle of deflection (rainbow angle) is measured at the point where the path of an incidence ray and the path of the same ray after it exits a raindrop towards the observer can be shown to intersect.
To make the incident and exiting ray intersect in a ray-tracing diagram the incident ray is extended forwards in a straight line beyond the raindrop. The ray exiting the droplet towards the observer is then extended backwards until both intersect. The angle of deflection (rainbow angle) lies between the two.
The angle of deflection (rainbow angle), for any ray that is contributing directly to the arcs of a primary rainbow, is always between approx. 40.70 and 42.40.
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.
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 rays 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.
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.