(1) The angle of deviation measures the angle between the direction of an incident ray and the direction of a refracted ray when light travels from one medium to another

(2) The angle of deviation measures the degree to which the path of light through a raindrop is altered in the course of refraction and reflection towards an observer.

###### About the angle of deviation (Raindrops)

- The angle of deviation is measured between the path of light incident to a raindrop and its path after it exits the raindrop back into air.
- In any particular example 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 light that forms a rainbow, if thought of in terms of rays, is approaching on trajectories 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 leaves a vacuum or travels 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 greater will be its angle of deviation.
- Amongst the optical properties of air and water, absorption, reflection, refraction, and scattering of light are the most important.
- It is the optical properties of raindrops that determine the angle of deviation of incident light as it exits a raindrop.
- It is the optical properties of raindrops that prevent any ray of visible light from exiting a primary raindrop at an angle of deviation less than 137.6
^{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 must reach an angle of deviation of at least 137.6
^{0}if it is to be visible to an observer. - 137.6
^{0 }is the angle of deviation that produces the appearance of red along the outside edge of a primary rainbow from the point of view of an observer. - 137.6
^{0 }is the minimum angle of deviation for any ray of visible light if it is to appear within a primary rainbow. - 139.3
^{0}is the angle of deviation 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 between 42.4^{0}(red) and 40.7^{0}(violet). - For any raindrop to form part of a primary rainbow it must be between the viewing angles of 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 must reach an angle of deviation of at least 137.6
- The range of angles of deviation that create the impression of colour for an observer is not related to droplet size.
- The laws of refraction (Snell’s law) and 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 making a small adjustment to the refractive index of water.

###### Minimum angle of deviation

- The optical properties of an idealised spherical raindrop mean that no light of any specific wavelength can deviate less than its minimum angle of deviation.
- The minimum angle of deviation for red light with a wavelength of approx. 720 nm is always 137.6
^{0}but similar rays with other points of impact can deviate up to a maximum of 180^{0}.^{ } - Imagine a falling raindrop:
- At a specific moment, the droplet is at an angle of 50
^{0}from the rainbow axis as seen from the point of view of an observer. This corresponds with an angle of deviation of 130^{0 }which is insufficient to be visible to an observer. - A moment later the droplet is at an angle of 42.4
^{0}which is the viewing angle for red in a primary rainbow so the droplet becomes visible to the observer. - 42.4
^{0 }corresponds with the rainbow angle for light with a wavelength of 720 nm, so at this moment the droplet appears red at maximum intensity. - As the droplet continues to fall, the minimum angle of deviation for red is passed and so that colour fades just as the minimum angle of deviation for orange arrives. For a second the same droplet now appears intensely orange.
- The sequence repeats for yellow, green, blue and then violet at which point the viewing angle drops below 40.7
^{0}. A moment later, it briefly produces ultra-violet light. - As soon as the minimum angle of deviation for violet is exceeded, increasing towards 180
^{0}, it no longer forms part of the arcs of colour seen by an observer, but continues to scatter light into the area between the bow and anti-solar point.

- At a specific moment, the droplet is at an angle of 50

###### By way of summary

- Raindrops emit no light of any particular wavelength at an angle less than its minimum angle of deviation.
- The minimum angle of deviation for any wavelength of visible light is never less than 137.6
^{0}whilst the maximum is always 180^{0}. - When the angle of deviation is 180
^{0}, the angles or refraction (on the entry and exit of a raindrop) = 0^{0 }and the angle of reflection = 180^{0}.