- The angle of deflection and the angle of deviation are always directly related to one another and together add up to 180
^{0}. - The angle of deflection is equal to 180
^{0}minus the angle of deviation. So clearly the angle of deviation is always equal to 180^{0}minus the angle of deflection. - In any particular case, the angle of deflection is always the same as the viewing angle because the incident rays of light that form a rainbow all approach on a trajectory running parallel with the rainbow axis.

##### Remember that:

- Any ray of light (stream of photons) travelling through empty space, unaffected by gravitational forces, travels in a straight line forever.
- When light travels from a vacuum or from one transparent medium into another, it undergoes refraction causing it to change both direction and speed.
- The more a ray changes direction as it passes through a raindrop the smaller will be the angle of deflection.
- It is the optical properties of raindrops that determine the angle of deflection of light as it exits a raindrop.
- Because of the optical properties of primary rainbows, no rays of light within the visible part of the electromagnetic spectrum exit a raindrop at an angle of deflection larger than 42.4
^{0}. - Because of the optical properties of secondary rainbows, no rays of light within the visible part of the electromagnetic spectrum exit a raindrop at an angle of deflection larger than 50.4
^{0}.

##### Now consider the following:

- For a single incident ray of light of a known wavelength striking a raindrop at a known angle:
- To appear in a primary rainbow it cannot exceed an
*angle of deflection*of more than 42.4^{0}. This corresponds with the*minimum angle of deviation*. - 42.4
^{0 }is the angle of deflection that produces the appearance of red along the outside edge of a primary rainbow from the point of view of an observer. - 180
^{0}– 137.6^{0 }= 42.4^{0 }is the maximum angle of deflection for any ray of visible light if it is to appear within a primary rainbow. - 180
^{0}-139.3^{0 }= 40.7^{0 }is the angle of deflection for a ray that appears violet along the inside edge of a primary rainbow. - Angles of deviation between 137.6
^{0}and 139.3^{0}correspond with viewing angles and angles of deflection between 42.4^{0}(red) and 40.7^{0}(violet). - An angle of deviation of 137.6
^{0}(so viewing angles of 42.4^{0}) corresponds with the appearance of red light with a wavelength of approx. 720 nm.

- To appear in a primary rainbow it cannot exceed an
- The range of angles of deflection that create the impression of colour for an observer is not related to droplet size.
- The laws of refraction (Snell’s law) and reflection and the law of reflection can be used to calculate the angle of deviation of white light in a raindrop.
- The angle of deviation can be fine-tuned for any specific wavelength by fine adjustment of the refractive index.

###### About rainbows: 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 angle between the original path of a ray of incident light prior to striking a raindrop and the angle of deviation.
- 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