Path of Parallel Rays Through a Raindrop
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.
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Path of Parallel Rays Through a Raindrop
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About the diagram
About the diagram
- Notice first of all that all the parallel incident rays shown in the diagram enter the top half of the raindrop above the horizontal axis, reflect once off the far side and exit downwards.
- This diagram shows yellow rays of the same wavelength passing through a raindrop.
- Because all the rays have the same wavelength, the refractive index for water used to calculate their path through the droplet can be fine-tuned to match.
- Because the refractive index is the same for every ray there is a consistent pattern to the way each ray changes direction and speed.
- The path of every ray is however different depending on the point of impact of each incident ray.
- The point of impact is measured on the parameter scale on the left. It shows that the incident rays have been organised incrementally between 0.0 and 1.0.
- More rays are shown between 0.7 and 1.0 because it is likely that the rainbow ray with the minimum angle of deviation will be among them.
- As explained further below, the term rainbow ray describes the path taken by the ray that produces the most intense colour experience for any particular wavelength of light passing through a raindrop.
- The minimum angle of deviation for a ray of light of any specific wavelength as it passes through a raindrop is the smallest angle to which it must change course before it becomes visible to an observer within the arcs of a rainbow.
- 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.
- 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.
Angle of deviation
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.
- 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
Internal reflection takes place when light travelling through a medium such as water fails to cross the boundary into another transparent medium such as air. The light reflects back off the boundary between the two media.
- Internal reflection is a common phenomenon so far as visible light is concerned but occurs with all types of electromagnetic radiation.
- For internal refraction to occur, the refractive index of the second medium must be lower than the refractive index of the first medium. So internal reflection takes place when light reaches air from glass or water (at an angle greater than the critical angle), but not when light reaches glass from air.
- In most everyday situations light is partially refracted and partially reflected at the boundary between water (or glass) and air because of irregularities in the surface.
- If the angle at which light strikes the boundary between water (or glass) and air is less than a certain critical angle, then the light will be refracted as it crosses the boundary between the two media.
- When light strikes the boundary between two media precisely at the critical angle, then light is neither refracted or reflected but is instead transmitted along the boundary between the two media.
- However, if the angle of incidence is greater than the critical angle for all points at which light strikes the boundary then no light will cross the boundary, but will instead undergo total internal reflection.
- The critical angle is the angle of incidence above which internal reflection occurs. The angle is measured with respect to the normal at the boundary between two media.
- The angle of refraction is measured between a ray of light and an imaginary line called the normal.
- In optics, the normal is an imaginary line drawn on a ray diagram perpendicular to, so at a right angle to (900), to the boundary between two media.
- If the boundary between the media is curved then the normal is drawn perpendicular to the boundary.
- As light travels from a fast medium such as air to a slow medium such as water it bends toward the normal and slows down.
- As light passes from a slow medium such as diamond to a faster medium such as glass it bends away from the normal and speeds up.
- In a diagram illustrating optical phenomena like refraction or reflection, the normal is a line drawn at right angles to the boundary between two media.
- A fast (optically rare) medium is one that obstructs light less than a slow medium.
- A slow (optically dense) medium is one that obstructs light more than a fast medium.
- The speed at which light travels through a given medium is expressed by its index of refraction.
- If we want to know in which direction light will bend at the boundary between transparent media we need to know:
- Which is the faster, less optically dense (rare) medium with a smaller refractive index?
- Which is the slower, more optically dense medium with the higher refractive index?
- The amount that refraction causes light to change direction, and its path to bend, is dealt with by Snell’s law.
- Snell’s law considers the relationship between the angle of incidence, the angle of refraction and the refractive indices (plural of index) of the media on both sides of the boundary. If three of the four variables are known, then Snell’s law can calculate the fourth.
- 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.
- 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.
- 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.
- In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (900), to the boundary between two media.
- If the boundary between the media is curved then the normal is drawn perpendicular to the boundary.
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