Path of Rays Through a Raindrop

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


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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
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.
Yes! Chromatic dispersion takes place as light crosses the boundary between one transparent medium and another if it has a different refractive index.
The wavelength of incident light decreases as it travels from air into a raindrop because water is an optically slower medium.

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

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

  • 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.

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.

Reflection takes place when incoming light strikes the surface of a medium, obstructing some wavelengths which bounce back into the medium from which they originated.

Reflection takes place when light is neither absorbed by an opaque medium nor transmitted through a transparent medium.

If the reflecting surface is very smooth, the reflected light is called specular or regular reflection.

Specular reflection occurs when light waves reflect off a smooth surface such as a mirror. The arrangement of the waves remains the same and an image of objects that the light has already encountered become visible to an observer.

Diffuse reflection takes place when light reflects off a rough surface. In this case, scattering takes place and waves are reflected randomly in all directions and so no image is produced.

  • A light source is a natural or man-made object that emits one or more wavelengths of light.
  • Natural light sources include:
    • The Sun is the most important natural 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 include:
    • 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
    • Tungsten lights: 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: These 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: These 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. Fluorescent lamps are very efficient at emitting visible light, produce less waste heat, and typically last much longer than incandescent lamps.
    • LED lights: An LED (Light Emitting Diode) is an electroluminescent light source. It produces light by passing an electrical charge across the junction of a semiconductor. An LED light typically emits a single colour of light which is composed of a very narrow range of wavelengths.
  • Made-made lights can emit a single wavelength, bands of wavelengths or combinations of wavelengths.

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