# Angles of Deviation – Table

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This is one of a set of almost 40 diagrams exploring Rainbows.

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• Follow the links embedded in the text for definitions of all the key terms.
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## Description

#### Angles of Deviation

###### TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
Deviation measures the degree to which raindrops cause sunlight to change direction in the process of its refraction and reflection back towards an observer. The position of raindrops in the sky and the amount of deviation determine whether the light will be visible to an observer.
The minimum angle of deviation of a ray of light of any specific wavelength passing through a raindrop is the smallest angle to which it must change course before it becomes visible within the arcs of a rainbow to an observer.

(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 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 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 137.60.
###### 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 137.60 if it is to be visible to an observer.
• 137.60 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.
• 137.60 is the minimum angle of deviation for any ray of visible light if it is to appear within a primary rainbow.
• 139.30 is the angle of deviation 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 between 42.40 (red) and 40.70 (violet).
• For any raindrop to form part of a primary rainbow it must be between the viewing angles of 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 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 137.60 but similar rays with other points of impact can deviate up to a maximum of 1800.
• Imagine a falling raindrop:
• At a specific moment, the droplet is at an angle of 500 from the rainbow axis as seen from the point of view of an observer. This corresponds with an angle of deviation of 1300 which is insufficient to be visible to an observer.
• A moment later the droplet is at an angle of 42.40 which is the viewing angle for red in a primary rainbow so the droplet becomes visible to the observer.
• 42.40 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 40.70. A moment later, it briefly produces ultra-violet light.
• As soon as the minimum angle of deviation for violet is exceeded, increasing towards 1800, 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.
###### 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 137.60  whilst the maximum is always 1800.
• When the angle of deviation is 1800, the angles or refraction (on the entry and exit of a raindrop) = 00 and the angle of reflection = 1800.

#### Some key terms

The angle of reflection measures the angle at which reflected light bounces off a surface.

• The angle of reflection is measured between a ray of light which has been reflected off a surface and an imaginary line called the normal.
• See this diagram for an explanation: Reflection of a ray of light
• In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (900), the boundary between two media.
• If the boundary between the media is curved then the normal is drawn perpendicular to the boundary.

The angle of refraction measures the angle to which light bends as it passes across the boundary between different media.

• The angle of refraction is measured between a ray of light and an imaginary line called the normal.
• In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (900), the boundary between two media.
• See this diagram for an explanation: Refraction of a ray of light
• If the boundary between the media is curved, the normal is drawn perpendicular to the boundary.

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.

• See this diagram for an explanation: Rainbow anatomy
• 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.

The angle of incidence measures the angle at which incoming light strikes a surface.

• The angle of incidence is measured between a ray of incoming light and an imaginary line called the normal.
• See this diagram for an explanation: Reflection of a ray of light
• In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (900), the boundary between two media.
• If the boundary between the media is curved, then the normal is drawn at a tangent to the boundary.

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