# Rainbow angle

The term rainbow angle is often paired with rainbow ray to measure the angle at which light is deflected back towards an observer as it passes through a raindrop.

• At lightcolourvision.org the term rainbow angle is avoided but is treated as being synonymous with the angle of deflection.
• 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.
• 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.