Angular distance

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 a cross-section of a rainbow in side elevation.
  • A cross-section of a rainbow in side elevation shows the sun, observer and the highest elevation of a rainbow above the horizon arranged along the rainbow axis.
  • Think of angular distance as an angle between 40.70 and 42.40 from the centre of a rainbow that accounts for the spectrum of colours between red and violet.
  • 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 within a primary bow is between approx. 40.70 and 42.40 from its centre.
  • The angular distance for any observed colour within a secondary bow is between approx. 50.40 and 53.40 when you are looking at 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 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.