A rainbow is a beautiful natural phenomenon that occurs when sunlight interacts with water droplets in the atmosphere. Rainbows appear as multicolored arcs across the sky, with red on the outer part of the arc and violet on the inner section. While rainbows may seem endless, extending beyond the horizon, they do actually have a beginning and end point. Understanding how rainbows are formed and the optics involved can help explain why rainbows visually appear endless but physically have finite boundaries.
How Rainbows Form
Rainbows are formed when sunlight enters a water droplet and is refracted (bent) and reflected internally on the droplet’s surface, with different wavelengths of light being separated. Here is a quick overview of how this happens:
- Sunlight is comprised of a continuous spectrum of colors from violet to red.
- When white sunlight enters a spherical water droplet, it is refracted upon entering, with each color bending at a slightly different angle based on its wavelength.
- The refracted light rays reflect off the back inner surface of the droplet and are refracted again when exiting.
- The combination of refraction and reflection separates the white light into its component color spectrum.
- An observer sees the varied colors of refracted light leaving multiple droplets, which form the rainbow.
So in summary, it is the process of light refracting, internally reflecting, and refracting again in myriad water droplets that creates the rainbow effect. But how does this produce the arc shape and make rainbows seem endless?
Optics of Rainbow Formation
Rainbows form optical arcs in the sky because of the specific angles involved in the internal reflection and refraction of light passing through spherical water droplets:
- Light enters a droplet at an angle between 0-180 degrees relative to the observer.
- The minimum angle for a rainbow is around 40 degrees.
- Light reflects internally at the back surface of the droplet at an angle of 42 degrees relative to the incoming rays.
- The refracted light leaves the droplet at an angle of 40-42 degrees relative to the incoming sunlight.
So there is only a narrow 2 degree window where the internal reflection and refraction produce the rainbow effect. Light entering droplets at less than 40 degrees is reflected internally, but does not refract back out. Above 42 degrees, light passes through but does not separate into a rainbow spectrum.
This narrow range of angles concentrates the rainbow colors into an arc formation centered on the antisolar point, which is directly opposite the sun from the observer’s perspective.
Why Rainbows Appear Endless
While physics shows that rainbows have a defined angular formation, there are several reasons rainbows appear to extend infinitely:
- The antisolar point is below the horizon for a ground-based observer, so the circular arc seems to stretch beyond the horizon line.
- A rainbow’s arc has a nearly constant angular radius, so as the observer’s distance increases, more of the arc comes into view.
- Light is refracted and reflected over a continuous region of the sky filled with droplets, so there is no obvious endpoint.
- The brightness and color intensity fade gradually rather than terminating abruptly.
Visually, these effects make the rainbow merge seamlessly into the landscape. But the physical and optical constraints mean rainbows cannot actually extend indefinitely.
Where Does a Rainbow End?
While rainbows appear limitless, there are distinct start and end points dictated by the optics involved:
- The bottom of the rainbow arc (bottom of the 41-42 degree ring) marks the start point of the rainbow.
- Antisolar point – The center of the circular rainbow arc, directly opposite the sun.
- Rainbow top – The uppermost point of the arc, at 42 degrees relative to the antisolar point.
- Alexander’s band – A darkened region between the main and secondary rainbows.
- Secondary rainbow – A second, fainter rainbow arc formed at 51 degrees from the antisolar point.
So in reality, rainbows exist as finite circular bands centered on the antisolar point. The main rainbow spans an angular radius of 42 degrees, with the secondary rainbow spanning 51 degrees. Beyond these bounds, rainbow colors and effects no longer occur.
The following diagram roughly illustrates the anatomical components of a rainbow:
| Rainbow Feature | Description |
|---|---|
| Bottom | Start of main arc, around 41 degrees from antisolar point |
| Antisolar Point | Center point opposite sun, 42-51 degrees from this point form rainbows |
| Rainbow Top | Topmost point of main arc, 42 degrees from antisolar point |
| Alexander’s Band | Dark band separating main and secondary rainbows |
| Secondary Rainbow | Second, fainter rainbow arc at 51 degrees |
So while rainbows may appear endless, optical geometry dictates finite boundaries. The rainbow effect only occurs within the 41-42 degree arc for the main rainbow and 51 degree arc for the secondary rainbow. Beyond these angular limits, rainbow colors and effects cease.
When Can Complete Rainbows Be Seen?
For a full, vivid rainbow to be visible, certain conditions are needed:
- Sun behind the observer, illuminating rain in front – Ideal antisolar point angle is 40-42 degrees.
- Rain or mist droplets sufficiently dispersed and dense.
- Bright sunlight and dark rain clouds to accentuate colors.
- Observer distance allows viewing a large portion of the arc.
Often rainbows are only partially visible since the ideal geometry is not achieved. Common partial rainbows include:
- Rainbow crest – Top portion visible when sun is relatively high.
- Rainbow smile – Bottom portion when sun is lower.
- Fogbows – Hazy rainbows in fog when droplets are very small.
So the positioning of the sun, ample rain and ideal viewing conditions are needed for a full rainbow extending from beginning to end to be observed.
Interesting Facts About Rainbow Endings
Some interesting trivia related to rainbow endings:
- Alexander’s band separating main and secondary rainbows is named after Alexander of Aphrodisias, who first described it in 200 AD.
- Moonbows, formed by moonlight rather than sunlight, also show the same optical ending points and angles.
- Double rainbows with reversed color order can form with the right droplet size distributions.
- Rainbows are centered on the antisolar point, so the observer sees different portions of the arc.
- Rainbows only exist when the sun angle relative to the observer is between 40-42 degrees.
So while visually tantalizing, rainbow physics and geometry dictate defined optical boundaries across the sky. The mythical pot of gold purported to lie at the end of the rainbow unfortunately has no factual basis! But the optical splendor and metaphoric symbolism of rainbows will continue inspiring awe, joy and imagination for generations to come.
Conclusion
In conclusion, while rainbows appear to extend indefinitely to the horizon and beyond, optical geometry defines clear angular boundaries. Rainbows can only form when sunlight is reflected and refracted in droplets at specific 40-42 degree angles relative to the antisolar point opposite the sun. This constrained 2 degree range concentrates the rainbow colors into a finite circular band in the sky. The main rainbow arc spans 41-42 degrees from the antisolar point, with the secondary arc extending to 51 degrees. Beyond these defined angular radii, rainbow effects cease. So despite the visual illusion of endlessness, physical optics limit rainbows to definitive start and end boundaries across the sky. Understanding the underlying meteorological optics provides deeper appreciation of nature’s wonderous display.
