Path of 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

To find out more about the diagram above . . . . read on!

Path of Rays Through a Raindrop

TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
The wavelength of incident light decreases as it travels from air into a raindrop because water is an optically slower medium.
Yes! Light travels faster in air than in water.
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.
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.
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.

About the diagram

About the diagram
  • This diagram shows rays passing through two identical raindrops.
  • Because all the rays have the same wavelength, the refractive index for water used to calculate their path through each 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.
  • Notice that all the parallel incident rays in the left-hand diagram enter the top half of the raindrop above the horizontal axis, reflect once off the far side and exit downwards.
  • Notice that all the parallel incident rays in the right-hand diagram enter the bottom half of the raindrop below the horizontal axis, reflect once off the far side and exit upwards.
  • As noted in the diagram, primary rainbows are formed by incident rays striking raindrops above their horizontal axis and reflecting once off the inside surface.
  • As the right-hand diagram shows incident rays striking raindrops below their horizontal axis and reflecting once off the inside surface can’t contribute to a primary rainbow because they direct rays upwards away from an observer.

Raindrops, incident light and primary rainbows

Let’s look at the rays of incident light that contribute to a primary rainbow.

  • All rays of light that contribute to a primary rainbow strike the surface of each raindrop three times. Once as they enter a droplet and undergo refraction, again as they reflect off the rear interior surface and once more as they undergo refraction for the second time and exit in the direction of the observer.
  • Whilst some photons are following paths that will produce a primary rainbow there are many other possibilities for every photon and the vast majority go off in other directions.
  • Incident rays of light that form the curved apex of a primary rainbow strike the upper half of raindrops in line with their vertical axis. These rays initially deviate downwards during refraction and internal reflection towards an observer.
    • Rays bend downwards (and slow down) as they enter a droplet and are refracted towards the normal.
    • Rays then reflect off the interior surface on the far side of a droplet and are directed downwards again.
    • When they strike the surface a third time, they are refracted away from the normal (and speed up) as they exit in the direction of the observer.
    • In some cases, this final step is an upward bend and so reduces the overall angle of deviation relative to their source.
  • Incident rays of light that form the curved sides of a primary rainbow strike the side of a raindrop in line with their horizontal axis. These rays initially deviate inwards during refraction and internal reflection towards an observer.
  • Incident rays of light striking the lower half of raindrops are initially directed upwards and away from the observer.
Raindrops, incident light and secondary rainbows

Now let’s look at the rays of incident light that contribute to a secondary rainbow.

  • All rays of light that contribute to a secondary rainbow strike the surface of each raindrop four times. Once as they enter a droplet and undergo refraction, twice as they reflect off the interior surface and once more as they undergo refraction for the second time and exit in the direction of the observer.
  • Incident rays of light that form the curved apex of a secondary rainbow strike the lower half of raindrops in line with their vertical axis. These rays initially deviate vertically upwards during refraction and internal reflection.
    • Rays bend upwards (and slow down) as they enter each droplet and are refracted towards the normal.
    • Rays then reflect twice off the interior surface on the far side of the droplet. After the second strike, they are directed downwards towards the observer.
    • Finally, at the fourth strike, they refract away from the normal (and speed up) as they exit.
  • Incident rays of light that form the curved sides of a secondary rainbow strike the side of a raindrop in line with their horizontal axis. These rays deviate inwards during refraction and internal reflection towards an observer.
  • Incident rays of light striking the upper half of raindrops at the apex of a rainbow during the formation of a secondary rainbow are initially directed downward and away from the observer.
Alexander’s band
  • The fact that light deviates downwards when it strikes the upper half of droplets that contribute to a primary rainbow and deviates upwards when it strikes the lower half of droplets that contribute to secondary bows accounts for the darker area between the two known as Alexander’s band.

Some key terms

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.

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.

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.

In the field of optics, dispersion is shorthand for chromatic dispersion which refers to the way that light, under certain conditions, separates into its component wavelengths, enabling the colours corresponding with each wavelength to become visible to a human observer.

  • Chromatic dispersion refers to the dispersion of light according to its wavelength or colour.
  • Chromatic dispersion is the result of the relationship between wavelength and refractive index.
  • When light travels from one medium (such as air) to another (such as glass or water) each wavelength is refracted differently, causing the separation of white light into its constituent colours.
  • When light undergoes refraction each wavelength changes direction by a different amount. In the case of white light, the separate wavelengths fan out into distinct bands of colour with red on one side and violet on the other.
  • Familiar examples of chromatic dispersion are when white light strikes a prism or raindrops and a rainbow of colours becomes visible to an observer.

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.

A light source is a natural or man-made object that emits one or more wavelengths of light.

  • The Sun is the most important light source in our lives and emits every wavelength of light in the visible spectrum.
  • Celestial sources of light include other stars, comets and meteors.
  • Other natural sources of light include lightning, volcanoes and forest fires.
  • There are also bio-luminescent light sources including some species of fish and insects as well as types of bacteria and algae.
  • Man-made light sources of the most simple type include natural tars and resins, wax candles, lamps that burn oil, fats or paraffin and gas lamps.
  • Modern man-made light sources include tungsten light sources. These are a type of incandescent source which means they radiate light when electricity is used to heat a filament inside a glass bulb.
  • Halogen bulbs are more efficient and long-lasting versions of incandescent tungsten lamps and produce a very uniform bright light throughout the bulb’s lifetime.
  • Fluorescent lights are non-incandescent sources of light. They generally work by passing electricity through a glass tube of gas such as mercury, neon, argon or xenon instead of a filament. These lamps are very efficient at emitting visible light, produce less waste heat, and typically last much longer than incandescent lamps.
  • An LED (Light Emitting Diode) is an electroluminescent light source. It produces light by passing an electrical charge across the junction of a semiconductor.
  • Made-made lights can emit a single wavelength, bands of wavelengths or combinations of wavelengths.
  • An LED light typically emits a single colour of light which is composed of a very narrow range of wavelengths.

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