Rainbows

Many of us have heard Judy Garland singing "Somewhere Over the Rainbow" in the classic movie The Wizard of Oz. A rainbow is such a beautiful sight that everyone is sure to experience it several times throughout their life. While the science behind it isn't as complex as some of the previous posts, I will try to explain everything as clearly as I can. In addition, I will include some history of the discovery of the rainbow along with common myths different groups of people held about its presence. As usual, I will begin by showing some personal photographs I captured of rainbows.








THE SCIENCE BEHIND RAINBOWS:
A rainbow cannot occur just anywhere in the sky. We have to be positioned just right, with our back to the sun and our front towards the rain in order to observe a rainbow. The sun has to be fairly low in the sky for the phenomena to occur. In fact, once the sun is 42 degrees above the horizon, all rainbows will disappear. There's an old saying that goes something like this,

"Red sky in morning, sailors take warning,
Red sky at night, a sailor's delight."

We can replace the words 'red sky' in this saying with 'rainbow' and still maintain the same meaning. Typically, rain moves from the west to the east in the middle-latitudes (that's where we are!). Since the sun rises in the east, using the logic presented earlier, a rainbow in the morning would mean rain lies to the west and is heading towards the observer. With the sun setting in the west, a rainbow at night would be to the observer's east and foreshadow a rain free night.

Simply put, we see rainbows due to the reflection and refraction of light in a raindrop. There is some mathematical complexities tied along with it, though. Using the picture below as a reference, if the angle between the refracted light and the normal to the drops surface is greater than the critical angle, the light reflects off the back of the raindrop. The critical angle for water happens to be 48 degrees. Therefore, if light strikes the back of the raindrop at an angle greater than 48 degrees, it is reflected back and refracted as it exits the raindrop. An angle less than 48 degrees would indicate that light passes through the drop without being reflected (no rainbow).


Photo Courtesy: http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/opt/wtr/rnbw/frm.rxml

At some point in our lifetime, we are taught the acronym ROY G BIV to remember the order of colors in the rainbow. For those who don't already know, that stands for Red, Orange, Yellow, Green, Blue, Indigo, and Violet. On a primary rainbow, red will appear on the top and violet on the bottom. The reason for this order can be explained with a little bit of math. Violet light bends the most and will emerge from the raindrop refracted at an angle of 40 degrees relative to the incoming sunlight. Red light bends the least, emerging at a mere 42 degrees. All the other colors emerge somewhere between 40-42 degrees. Now wait a minute, you might be scratching your head realizing that based on those numbers, red would appear on the bottom and violet would appear on the top. While this might not make a whole lot of sense, we actually view red light coming from drops higher in the sky, and violet light from the drops that are lower. For every raindrop, only one color of light can be observed from it. That means it takes millions of raindrops acting like tiny prisms to make up a rainbow. No one person view the same rainbow as you do, in the sense that what light you see refracting towards you comes from different raindrops than the person who's standing next to you. So now that we understand why we see the spectrum in the sky, what determines the brightness or dullness of the light in a rainbow? It has to do with the size of the raindrops the sunlight is being reflected on. Larger raindrops will typically produce a brighter rainbow.

It is not uncommon to sometimes see what some people call a double rainbow. The technical name for this is actually a secondary rainbow; and while it's similar to the primary rainbow, it carries with it some key differences. Let's first observe a picture of a real life primary and secondary rainbow.


Photo Courtesy: http://www.trekearth.com/gallery/North_America/United_States/West/Wyoming/douglas/photo19837.htm

You will notice in the picture that the secondary rainbow occurs above the primary rainbow. The colors on the secondary rainbow are the reverse of the primary, with red being on the bottom and violet being on top. You will also notice that the coloring on the second rainbow is much fainter than the first. The level or brightness and color reversion can be attributed to the simple science that two internal reflections are occurring instead of just one. Also take notice of the darker band in between the two bows. This is called Alexander's band, named after Alexander of Aphrodisias, who was the first to describe this phenomena back in 200 AD. Now I want you to take a look at the picture below. It is a snapshot from one of my favorite movies, A Perfect Getaway. Whoever was in charge of this scene obviously did not brush up on their science beforehand. The secondary rainbow is not reversed as it should be, and the primary rainbow is not the brighter of the two. Just a little flick flub I thought I'd throw in here for you, keep your eye out for another mishap like this when a film decides to display a double rainbow!


Incorrect display of primary and secondary rainbow in the 2009 film A Perfect Getaway.


THE DISCOVERY OF RAINBOWS, a brief history:
Aristotle is believed to be the first to try to describe a rainbow. He presumed that a rainbow was caused by the reflection of sunlight in clouds, which turned out to be incorrect. But he was able to explain the circular shape and say that a rainbow is not located in a definite place in the sky. In 1266, Roger Bacon mathematically measured the angle of a rainbow cone to be 42 degrees, with the secondary bow occurring 8 degrees higher. It wasn't until 1304 that a German monk, Theodoric of Freiberg, proposed that each raindrop in a cloud makes its own rainbow. He verified this with the diffraction of sunlight in a circular bottle, but his results were unknown until Rene Descartes rediscovered diffraction of a drop in 1656. Both of these men were aware that two bows existed, and that the reflection happened once in the primary bow and twice in the secondary bow.


A RAINBOW OF MYTHS:
I came across a site that listed several different myths that people from around the world believed at one point or another. I'll present them in a list so that they are easier to comprehend.

Christians: believe the rainbow was put in the sky by God as a covenant with Noah that He'd never destroy the earth by flood again
Mayans: belief similar to the Christians, however their world was destroyed by fire rain and those who escaped saw the rainbow as a symbol that the anger of the gods had ended
Norse & Navajo: the rainbow represented the distance between heaven and earth; it was the gateway or bridge to heaven that occurred when St. Peters opens the pearly gates. The Norse believed the bridge could only be used by gods or those who were killed in a just battle.
Buddhists: related the 7 colors of the rainbow to the 7 regions of earth. They viewed the rainbow as the next highest state achievable before Nirvana.
Islam: only had four colors in their rainbow (blue, green, red, yellow) and related them to the four elements of earth, water, wind, and fire
Hindu: believed a rainbow represented the archer's bow of their god of war and that he used the bow to shoot arrows of lightning to kill demons that threatened their land and people
Germanic mythology: the rainbow is the bowl that God used during creation to color the world
Incas: gift from the sun god
Arabians: a rainbow was tapestry woven by the south wind
Irish: believed leprechauns held a pot of gold at the end of the rainbow
Polish: similar to the Irish, but believed the gold was a gift by angels for the person who found it
Cherokees: believed it to be the hem of their sun god's coat
Aborigines: represented the Rainbow Serpent Mother, who was their goddess of creation
Greece: a rainbow is the symbol of the goddess Iris, who is also the goddess of healing
Roman mythology: the rainbow was the pathway used by the messenger god, Mercury
Honduras/Nicaragua: viewed the rainbow as a symbol of the devil and hid in their homes till it passed; believed looking at it put a curse on them
Japan: at some point in the past, the presence of a rainbow was a bad luck omen because it reminded them of snakes (which they considered evil)
Slavic mythology: a mortal touched the rainbow and was turned into a demonic-creature by the god of lightning and thunder

And finally.... WELCOME TO AGGIELAND!


Sources:
Ahrens, C. Donald. "Light, Color, and Atmospheric Optics." Meteorology Today: an Introduction to Weather, Climate, and the Environment. Belmont, CA: Brooks/Cole, CengageLearning, 2009. 542-544. Print.
Burroughs, William James., and Richard Whitaker. Weather. San Francisco, CA: Fog City, 2007. 256-257. Print.
"The History of the Rainbow." Carl Hemmingsens Software. Web. 24 Aug. 2010. http://www.datalyse.dk/Rainbow/history.htm.
Kuchinsky, Charlotte. "The Rainbow & the Various Myths Surrounding It, Page 3 of 3." Associated Content - Associatedcontent.com. 7 Dec. 2007. Web. 24 Aug. 2010. http://www.associatedcontent.com/article/466052/the_rainbow_the_various_myths_surrounding_pg3.html?cat=34.
Morgan, Sally, and David Ellyard. "Weather Wonders." Weather. [Alexandria, Va.]: Time-Life, 1996. 28-29. Print.
"Rainbows: an Arc of Concentric Colored Bands." WW2010 (the Weather World 2010 Project):. Web. 24 Aug. 2010. http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/opt/wtr/rnbw/frm.rxml.