- Angular distance, viewing angle, and angle of deflection are related concepts that produce similar values, expressed in degrees.
- Angular distance is one of the angles measured on a ray-tracing diagram that illustrates the sun, an observer, and a rainbow from a side view.
- Think of angular distance as the angle between the line to the centre of a rainbow down which an observer looks and the line to a specific colour in its arc. The red light is deviated by about 42.4° and violet light by about 40.7°.
- Angular distances for different colours are fairly constant, determined by the laws of refraction and reflection inside the water droplets.
- The sun’s position, the observer’s location, and the specific location of rainfall all influence where a rainbow will appear from an observer’s perspective.
- The coloured arcs of a rainbow form parts of circles (discs or cones), and all these circles share a common centre—the observer’s anti-solar point, which is directly opposite the sun.
- The angular distance to a specific colour is consistent, regardless of the point chosen along the arc of that colour in the rainbow.
- The angular distance for any observed colour in a primary rainbow varies from approximately 42.4° for red to 40.7° for violet.
- The angular distance for any observed colour in a secondary rainbow ranges from about 53.4° for red to 50.4° for violet, measured from the antisolar point.
- The angular distance for any specific colour within a rainbow can indeed be calculated, depending on its wavelength and how it refracts within the water droplets.
- From an observer’s viewpoint, all the incoming light rays seen by the observer appear parallel to 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.
- Many of the light rays that strike a raindrop follow paths that place them outside the range of possible viewing angles, so do contribute to the coloured arcs seen by an observer.

###### About viewing angles, angular distance and angles of deflection

- The term
*viewing angle*refers to the angle, measured in degrees, between the direction an observer looks in to see the centre of the rainbow and the direction they look to see a specific colour within the rainbow’s arc. - The term
*angular distance*refers to the same measurement as the viewing angle, especially when depicted on a side elevation diagram. - The
*angle of deflection*measures the change in direction that a light ray undergoes as it strikes, refracts into, reflects inside, and refracts out of a raindrop towards an observer. - The term
*rainbow ray*refers to the path taken by a deflected light ray that results in the most intense colour perception for a specific wavelength of light passing through a raindrop. - The term
*angle of deviation*measures the change in direction a light ray undergoes due to refraction and reflection inside a raindrop, relative to its original direction towards an observer.- In any specific case of a light ray passing through a raindrop, the
*angle of deviation*and the*angle of deflection*are interrelated and their sum equals 180^{0}. - The angle of deviation is equal to 180
^{0 }minus the angle of deflection, and vice versa, so the*angle of deflection*is equal to 180^{0 }minus the angle of deviation. - In any specific instance, the
*angle of deflection*is approximately the same as the*viewing angle*, because the incident light rays that contribute to a rainbow all approach parallel to the axis of the rainbow.

- In any specific case of a light ray passing through a raindrop, the

- See this diagram for an explanation: Angular distance & Raindrop colour
- Angular distance is one of the angles measured on a ray-tracing diagram that illustrates the sun, an observer, and a rainbow from a side view.
- Think of angular distance as the angle between the line to the centre of a rainbow down which an observer looks and the line to a specific colour in its arc. The red light is deviated by about 42.4° and violet light by about 40.7°.