# Angular distance

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.