# Angle of deflection

When discussing the formation of rainbows, the angle of deflection measures the angle between the initial path of a light ray before it hits a raindrop, and the angle of deviation, which measures how much the ray bends 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 180 degrees.
• The angle of deflection equals 180 degrees minus the angle of deviation. So, it’s clear the angle of deviation is always equal to 180 degrees 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 follow paths that run parallel with the rainbow axis.
##### Related Points
• Any ray of light (stream of photons) travelling through empty space, unaffected by gravity, 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 light ray changes direction when it passes through a raindrop, the smaller the angle of deflection will be.
• 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 degrees.
• 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 degrees.
##### Implications of the Angle of Deflection for Raindrops
•  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 degrees. This corresponds with the minimum angle of deviation.
• 42.40 is the angle of deflection that results in red appearing along the outside edge of a primary rainbow from the point of view of an observer.
• 180 degrees minus 137.6 degrees equals 42.4 degrees, which is the biggest angle of deflection for any visible light ray if it is to appear within a primary rainbow.
• 180 degrees minus 139.3 degrees equals 40.7 degrees, which is the angle of deflection for a light ray that appears violet and forms the inside edge of a primary rainbow.
• Angles of deviation between 137.6 degrees and 139.3 degrees match viewing angles and angles of deflection between 42.4 degrees (red) and 40.7 degrees (violet).
• An angle of deviation of 137.6 degrees (so viewing angles of 42.4 degrees) matches the appearance of red light with a wavelength of about 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 can be used to work out the angle of deviation of white light in a raindrop.
• The angle of deviation can be fine-tuned for any specific wavelength by making small adjustments to the refractive index.
##### How they interconnect
• 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 to the rainbow axis.