# Angle of deflection

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 which measures the degree to which the ray is bent back on itself in the course of refraction and reflection towards an observer.

• The angle of deflection and the angle of deviation are always directly related to one another and together add up to 1800.
• The angle of deflection is equal to 1800 minus the angle of deviation. So clearly the angle of deviation is always equal to 1800 minus the angle of deflection.
• 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 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 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 deflection larger than 42.70.
###### 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 42.70. This corresponds with the minimum angle of deviation.
• 42.70 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.
• 1800 – 137.60 = 42.0 4 is the maximum angle of deflection for any ray of visible light if it is to appear within a primary rainbow.
• 1800 -139.30 =  40.70 is the angle of deflection for a ray that appears violet along the inside edge of a primary rainbow.
• Angles of deviation between 137.60 and 139.30 correspond with viewing angles and angles of deflection between 42.40 (red) and 40.70 (violet).
• An angle of deviation of 137.60 (so viewing angles of 42.40) corresponds with the appearance of red light with a wavelength of approx. 720 nm.
• 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.
###### 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 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.