Angle of Deviation

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


Each diagram appears on a separate page and is supported by a full explanation.

  • Follow the links embedded in the text for definitions of all the key terms.
  • For quick reference don’t miss the summaries of key terms further down each page.

Description

Angle of Deviation

TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
Incident light refers to incoming light that is travelling towards an object or medium.
_x000D_ _x000D_ Reflection takes place when incoming light strikes the surface of a medium, some wavelengths are obstructed, and the wavefront bounces off and returns into the medium from which it originated.
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.

About the diagram

About the top diagram
  • The diagram at the top of the page shows the paths taken by parallel rays of yellow light striking a raindrop at different points on its surface.
  • The rays correspond with 0.8 to 0.9875 on the impact parameter scale.
  • This is a measured drawing and the angles shown are indicative of the path of parallel yellow rays with a wavelength of 589.29nm travelling through water water at 200C.
  • The paths have been calculated using refractive indices for air = 1.000293 and for water = 1.333.
  • Each path has been drawn as accurately as possible using simple geometry (in the absence of an equation that calculates the angles). A table showing all the angles can be seen here.
  • The bright yellow path at 8.50 on the impact parameter scale corresponds with the ray with the minimum angle of deviation. This ray is the rainbow ray.
About the carousel of diagrams
  • The carousel contains 20 diagrams showing the paths taken by identical yellow rays striking a raindrop over the full range of the impact parameter scale.
  • To view the images at their best we recommend downloading the set here and viewing them on separate tabs of a browser (eg. Chrome or Firefox).
  • These are measured drawing and all the angles shown are indicative of the path of parallel yellow rays with a wavelength of 589.29nm travelling through water water at 200C.
  • The paths have been calculated using refractive indices for air = 1.000293 and for water = 1.333.
  • A table showing all the angles can be seen here.
Angle of deviation

(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.
Rainbow ray
  • Rainbows are composed of rainbow rays.
  • Rainbow rays are responsible for an observer’s perception of a rainbow.
  • Rainbow rays are rays of light of a single wavelength that have their origin in individual raindrops. They can be explained in terms of their angular distance from the rainbow axis at the moment they contribute to an observer’s view of a rainbow.
  • Rainbow rays are ephemeral. They are not individually observable but more a way of conceptualizing the fact that at a specific moment and in a specific position a raindrop will transmit one spectral colour towards an observer before falling further, perhaps to reappear in a different position and another colour.
  • Individual rainbow rays produce the intense appearance of each of the different spectral colours that together constitute the phenomenon of rainbows.
  • Rainbows are composed of millions of rainbow rays and each one has its origin within a single raindrop.
  • A rainbow ray is a ray of a single wavelength that for a second is responsible for a bright flash of its corresponding colour as a result of being in exactly the right place at the right time.
  • Rainbow rays are always located amongst the rays that deviate the least as they pass through a raindrop and bunch together around the minimum angle of deviation.
  • The millions of microscopic images of the Sun that produce the impression of a rainbow function in a similar way to the pixels that produce the images we see on digital displays.
  • Rainbow rays tend to out-shine all other sources of light in the sky (other than the Sun) and account for the brilliance and imposing appearance of rainbows.
  • Because raindrops polarize light at a tangent to the circumference of a rainbow, the path of rainbow rays dissects raindrops exactly in half.
  • So:
    • Individual rainbow rays account for the appearance of spectral colours of a single wavelength within the arcs of a rainbow.
    • Bands of colour within a rainbow are composed of rainbow rays that together transmit narrow spreads of wavelengths towards an observer.
    • The overall appearance of a rainbow as a singular phenomenon can be accounted for by optical and geometric rules that determine the passage of light through raindrops and in the process account for rainbow rays.
  • Remember: the notion of light rays and rainbow rays are useful when considering the path of light through different media in a simple and easily understandable way. But in the real world, light is not really made up of rays. More accurate descriptions use terms such as photons or electromagnetic waves.

Some key terms

The angle of reflection is the angle between the incident light ray and the reflected light ray, both measured from an imaginary line called the normal.

  • According to the law of reflection, the angle of incidence (the angle between the incident ray and the normal) is always equal to the angle of reflection.
  • The angle of reflection is measured between the reflected ray of light and an imaginary line perpendicular to the surface, known as the normal.
  • In optics, the normal is a straight line drawn on a ray-tracing diagram at a 90º angle (perpendicular) to the boundary where two different media meet.
  • Expressed more formally, in optics, the normal is a geometric construct, a line drawn perpendicular to the interface between two media at the point of contact. This conceptually defined reference line is crucial for characterizing various light-matter interactions, such as reflection, refraction, and absorption.
  • If the boundary between two media is curved, the normal is drawn perpendicular to the tangent to that point on the boundary.
  • Reflection can be diffuse (when light reflects off rough surfaces) or specular (in the case of smooth, shiny surfaces), affecting the direction of reflected rays.
  • 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 reflection measures the angle at which light rebounds from a surface after being reflected.

  • 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.
  • 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.
  • The angle of reflection can be used to understand how light will behave when it interacts with different types of surfaces and objects.

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

  • The angle of refraction is measured between the bent ray 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.
  • Snell’s law is a formula used to describe the relationship between the angle of incidence and the angle of refraction when light crosses the boundary between transparent media, such as water and air or water and glass.

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

  • When light is travelling towards something it is said to be incident to that surface or object.
  • The angle of incidence is measured between a ray of incoming 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.
  • Expressed more formally, in optics, the normal is a geometric construct, a line drawn perpendicular to the interface between two media at the point of contact. This conceptually defined reference line is crucial for characterizing various light-matter interactions, such as reflection, refraction, and absorption.
  • Incident light may have travelled from the Sun or a man-made source or may have already been reflected off another surface such as a mirror.
  • When incident light strikes a surface or object it may undergo absorption, reflection, refraction, transmission or any combination of these optical effects.
  • 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.

The angle of incidence refers to the angle at which incoming light strikes a surface and is measured between a ray of incoming 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.
  • The angle at which incident light from the Sun or a light bulb strikes a surface can affect the outcome. For instance, when incident light hits a mirror, the angle of incidence determines the angle of reflection.

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