Path of 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.
- Follow the links embedded in the text for definitions of all the key terms.
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Path of Rays Through a Raindrop
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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
- 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.
- 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
Dispersion (or chromatic dispersion) refers to the way that light, under certain conditions, separates into its component wavelengths and the colours corresponding with each wavelength become visible to a human observer.
- Dispersion is the result of the relationship between refractive index and wavelength.
- Every wavelength of light is affected to a different degree by the refractive index of a medium. The result is that each wavelength changes direction and speed by a different amount.
- In the case of white light, the separate wavelengths span out with red at one end and violet at the other.
- A familiar example of dispersion is when white light strikes raindrops and a rainbow of colours becomes visible to an observer.
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.
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.
- 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.
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