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.