Path of Parallel Rays Through a Raindrop

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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

Path of Parallel Rays Through a Raindrop

TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
Rainbows are at their best early morning and late afternoon when a shower has just passed over and the Sun is illuminating the curtain of raindrops formed on the trailing edge of the falling rain.
The wavelength of incident light decreases as it travels from air into a raindrop because water is an optically slower medium.
Yes! Every wavelength of light is affected to a different degree by the refractive index of a transparent medium and as a result, changes direction by a different amount when passing from air to water or water to air.
Yes! Light travels faster in air than in water.

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.
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.
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.

Some key terms

  • The observer effect is a principle of physics and states that any interaction between a particle and a measuring device will inevitably change the state of the particle. This is because the act of measurement itself imposes a disturbance on the particle’s wave function, which is the mathematical description of its state.
  • The concept of observation refers to the act of engaging with an electron or other particle, achieved through measuring its position or momentum.
  • In the context of quantum mechanics, observation isn’t a passive undertaking, observation actively alters a particle’s state.
  • This means that any kind of interaction with an atom, or with one of its constituent particles, that provides insight into its state results in a change to that state. The act of observation is always intrusive and will always change the state of the object being observed.
  • It can be challenging to reconcile this with our daily experience, where we believe we can observe things without inducing any change in them.

Internal reflection occurs when light travelling through a medium, such as water or glass, reaches the boundary with another medium, like air, and a portion of the light reflects back into the original medium. This happens regardless of the angle of incidence, as long as the light encounters the boundary between the two media.

  • Internal reflection is a common phenomenon not only for visible light but for all types of electromagnetic radiation. For internal reflection to occur, the refractive index of the second medium must be lower than that of the first medium. This means internal reflection happens when light moves from a denser medium, such as water or glass, to a less dense medium, like air, but not when light moves from air to glass or water.
  • In everyday situations, light is typically both refracted and reflected at the boundary between water or glass and air, often due to irregularities on the surface. If the angle at which light strikes this boundary is less than the critical angle, the light is refracted as it crosses into the second medium.
  • When light strikes the boundary exactly at the critical angle, it neither fully reflects nor refracts but travels along the boundary between the two media. However, if the angle of incidence exceeds the critical angle, the light will undergo total internal reflection, meaning no light passes through, and all of it is reflected back into the original medium.
  • The critical angle is the specific angle of incidence, measured with respect to the normal (a line perpendicular to the boundary), above which total internal reflection occurs.
  • In ray diagrams, the normal is an imaginary line drawn perpendicular to the boundary between two media, and the angle of refraction is measured between the refracted ray and the normal. If the boundary is curved, the normal is drawn perpendicular to the curve at the point of incidence.

Refraction refers to the way that electromagnetic radiation (light) changes speed and direction as it travels across the boundary between one transparent medium and another.

  • Light bends towards the normal and slows down when it moves from a fast medium (like air) to a slower medium (like water).
  • Light bends away from the normal and speeds up when it moves from a slow medium (like diamond) to a faster medium (like glass).
  • These phenomena are governed by Snell’s law, which describes the relationship between the angles of incidence and refraction.
  • The refractive index (index of refraction) of a medium indicates how much the speed and direction of light are altered when travelling in or out of a medium.
  • It is calculated by dividing the speed of light in a vacuum by the speed of light in the material.
  • Snell’s law relates the angles of incidence and refraction to the refractive indices of the two media involved.
  • Snell’s law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices.

Total internal reflection occurs when light travelling through a denser medium strikes a boundary with a less dense medium at an angle exceeding a specific critical angle. As a result, all the light is reflected back into the denser medium, and no light transmits into the second medium.

  • Total Internal reflection only takes place when the first medium (where the light originates) is denser than the second medium.
  • The critical angle is the angle of incidence above which total internal reflection occurs.
  • The critical angle is measured with respect to the normal.
    • The normal is an imaginary line drawn in a ray diagram perpendicular to, so at a right angle to (900), to the boundary between two media.

Reflection is the process where light rebounds from a surface into the medium it came from, instead of being absorbed by an opaque material or transmitted through a transparent one.

  • The three laws of reflection are as follows:
    • When light hits a reflective surface, the incoming light, the reflected light, and an imaginary line perpendicular to the surface (called the “normal line”) are all in the same flat area.
    • The angle between the incoming light and the normal line is the same as the angle between the reflected light and the normal line. In other words, light bounces off the surface at the same angle as it came in.
    • The incoming and reflected light are mirror images of each other when looking along the normal line. If you were to fold the flat area along the normal line, the incoming light would line up with the reflected light.

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.

A human observer is a person who engages in observation by watching things.

  • In the presence of visible light, an observer perceives colour because the retina at the back of the human eye is sensitive to wavelengths of light that fall within the visible part of the electromagnetic spectrum.
  • The visual experience of colour is associated with words such as red, blue, yellow, etc.
  • The retina’s response to visible light can be described in terms of wavelength, frequency and brightness.
  • Other properties of the world around us must be inferred from light patterns.
  • An observation can take many forms such as:
    • Watching an ocean sunset or the sky at night.
    • Studying a baby’s face.
    • Exploring something that can’t be seen by collecting data from an instrument or machine.
    • Experimenting in a laboratory setting.

 

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.

Incident light refers to light that is travelling towards an object or medium.

  • Incident light refers to light that is travelling towards an object or medium.
  • Incident light may come from the Sun, an artificial source or may have already been reflected off another surface, such as a mirror.
  • When incident light strikes a surface or object, it may be absorbed, reflected, refracted, transmitted or undergo any combination of these optical effects.
  • Incident light is typically represented on a ray diagram as a straight line with an arrow to indicate its direction of propagation.

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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