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 42.4
^{0}and violet at 40.7^{0}. - 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 42.4
^{0}and violet at 40.7^{0}. - The angular distance for any observed colour in a secondary bow is between 53.4
^{0}and 50.4^{0}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. - 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 180^{0}. - The angle of deviation is always equal to 180
^{0}minus the angle of deflection. So clearly the angle of deflection is always equal to 180^{0}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.

- In any particular example of a ray of light passing through a raindrop, the